Question 1

The point toward which compasses on the earth's surface point is a magnetic south pole.

Accepted Answer

The magnetic south pole is the point on the Earth's surface where the Earth's magnetic field lines point vertically downward. Compasses on the Earth's surface point towards the magnetic south pole.

Question 2

Imagine a small magnet (with its north pole vertically upward) passing near the north pole of an external magnet that is below the small magnet. In what direction does the net force acting on the magnet point?

Accepted Answer

The net force points downward due to the repulsive force between the like poles (north pole of the small magnet and north pole of the external magnet).

Question 3

Imagine a small magnet with its north pole vertically upward passing near the south pole of an external magnet that is above the small magnet. In what direction does the net force acting on the magnet point?

Accepted Answer

The net force on the small magnet points upward because opposite magnetic poles attract each other. In this scenario, the north pole of the small magnet is attracted to the south pole of the external magnet above it, resulting in an upward force.

Question 4

It is possible with appropriately shaped external magnetic poles to create a situation where the effect of those poles does not vary with position along the SG axis. Imagine a small magnet placed in such a situation. What is the direction of the net force on the small magnet?

Accepted Answer

In a uniform magnetic field, the forces on the opposite poles of a small magnet are equal and opposite, resulting in no net force on the magnet regardless of its orientation. The magnetic field exerts forces on both poles of the magnet that cancel out, leading to zero net force.

Question 5

The direction of the net force on a small magnet will be the same if the SG axis is reversed and the effect of the external magnet decreases in the axis direction instead of increasing.

Accepted Answer

The net force on a small magnet is determined by the vector sum of the magnetic forces due to the external magnet and the Earth's magnetic field. If the SG axis is reversed, the direction of the magnetic force due to the external magnet will be reversed, but the direction of the magnetic force due to the Earth's magnetic field will remain the same. Therefore, the direction of the net force will be the same. If the effect of the external magnet decreases in the axis direction instead of increasing, the magnitude of the net force will decrease, but the direction will remain the same.

Question 6

A tilted top that is spinning clockwise (when viewed from above) experiences a torque that is always horizontal and perpendicular to the top's angular momentum. If initially the top's axis of rotation leans somewhat to the viewer's right and the torque points toward the viewer, how will the top's axis of rotation precess around the vertical direction?

Accepted Answer

The top's axis of rotation will precess counter-clockwise when viewed from above due to the right-hand rule, which relates the direction of the torque (toward the viewer), the angular momentum (to the viewer's right), and the resulting precession (counter-clockwise from above).

Question 7

A muon is exactly like an electron (including having $|\vec{s}|=\frac{1}{2} \hbar$ )except it is 207 times as massive. The classical model of spin would imply that a muon rotates

Accepted Answer

The answer of A muon is exactly like an electron...

Question 8

The drawing below shows a sequence of Stern-Gerlach devices. By analogy to the cases discussed in the chapter, what do you think are the probabilities that an electron entering the last device will come out of that device's plus and minus channels, respectively?

Accepted Answer

The answer of The drawing below shows a sequence of...

Question 9

The drawing below shows a sequence of Stern-Gerlach devices. By analogy to the cases discussed in the chapter, what do you think are the probabilities that an electron entering the last device will come out of that device's plus and minus channels, respectively?

Accepted Answer

The answer of The drawing below shows a sequence of...

Question 10

Figure Q6.15 below shows a sequence of Stern-Gerlach devices. By analogy to the cases discussed in the chapter, what do you think are the probabilities that an electron entering the last device will come out of that device's plus and minus channels, respectively?

Accepted Answer

The answer of Figure Q6.15 below shows a sequence of...

Question 11

Which of the following is a valid spin state $q$-vector? (If you are using the letters on the back cover, you can indicate more than one choice by pointing to several letters.)

Accepted Answer

A valid spin state $q$-vector must have a magnitude of 1. Option B satisfies this condition as $(-1/2)^2 + (\sqrt{3/4})^2 = 1$.

Question 12

Consider a set of electrons with an initial spin state
$$|\psi\rangle=\left[\begin{array}{c}
\sqrt{1 / 2} \
\sqrt{1 / 2}
\end{array}\right]$$
If we send these electrons into an SGx device, what is the probability that a given electron will be determined to have its spin anti aligned with the $+x$ direction?

Accepted Answer

The answer of Consider a set of electrons with an...

Question 13

Consider a set of electrons with an initial spin state
$$|\psi\rangle=\left[\begin{array}{l}
0 \
1
\end{array}\right]$$
If we send these electrons into an SGx device, what is the probability a given electron will be determined to have its spin anti aligned with the $+x$ direction?

Accepted Answer

The given initial spin state $|\psi\rangle = \left[\begin{array}{l} 0 \ 1 \end{array}\right]$ represents a spin-down state in the z-direction. When measuring the spin in the x-direction, the probabilities are determined by projecting this state onto the eigenstates of the $S_x$ operator. The eigenstates of $S_x$ for spin $+\frac{1}{2}$ and $-\frac{1}{2}$ (aligned and anti-aligned with the x-direction, respectively) are equal superpositions of the z-basis states, but with different phase factors for the spin-up and spin-down components. The probability of finding the electron in either state (aligned or anti-aligned) is the square of the amplitude of the projection of $|\psi\rangle$ onto the respective eigenstate of $S_x$. Since the initial state is a pure z-direction spin-down state, it is an equal superposition of the x-direction spin states, leading to a $1/2$ probability of finding the electron spin anti-aligned with the $+x$ direction.

Question 14

Imagine that an electron with an initial spin state
$$|\psi\rangle=\left[\begin{array}{l}
\sqrt{1 / 2} \
\sqrt{1 / 2}
\end{array}\right]$$
Goes into an SGz device and comes out the - channel of that device. The electron's spin state is now

Accepted Answer

The SGz device separates electrons based on their spin along the z-axis. The - channel corresponds to spin down, which is represented by the state vector $\left[\begin{array}{l}0 \ 1\end{array}\right]$, indicating the electron's spin is now in the down state.

Question 15

Imagine that an electron with an initial spin state
$$|\psi\rangle=\left[\begin{array}{c}
\frac{3}{5} \
-\frac{4}{5}
\end{array}\right]$$
Goes into an SGx device and comes out the - channel of that device. The electron's spin state is now

Accepted Answer

The SGx device measures the spin along the x-axis. The eigenstates for spin along the x-axis are $\frac{1}{\sqrt{2}}\left[\begin{array}{c}1 \ 1\end{array}\right]$ for the + channel and $\frac{1}{\sqrt{2}}\left[\begin{array}{c}1 \ -1\end{array}\right]$ for the - channel. Since the electron comes out the - channel, its state is aligned with the - eigenstate, which matches choice C.

Question 16

Consider the sequence of SG devices shown in figure Q7.7. Which of the expressions below gives the proper quantum amplitude that an electron emerging from the first SG device leaves via the - channel of the final device? (Do not assume that the inner product is commutative.)

Figure 07.7

Accepted Answer

The answer of Consider the sequence of SG devices shown...

Question 17

Consider the following quantum state vector:
$$|\psi\rangle=\left[\begin{array}{c}
\frac{3}{5} \
-\frac{4}{5}
\end{array}\right]$$
Which of the following $q$-vectors is physically equivalent to the vector $|\psi\rangle$ ?

Accepted Answer

The answer of Consider the following quantum state vector:
$$|\psi\rangle=\left[\begin{array}{c}
\frac{3}{5} \
-\frac{4}{5}
\end{array}\right]$$
Which...

Question 18

Suppose that a quanton's energy is zero, irrespective of its spin orientation. Suppose further that we prepare this quanton in an arbitrary spin state $|\psi(0)\rangle$. The probability of any possible experimental outcome for any spin observable will then be independent of time.

Accepted Answer

The time evolution of a quantum state is governed by the Schrödinger equation, and if the energy of the quanton is zero, the state will not evolve with time. Therefore, the probability of any experimental outcome for any spin observable, which depends on the state of the system, will remain constant over time.

Question 19

We can completely determine a $q$-vector's components from an appropriate set of probability measurements.

Accepted Answer

A $q$-vector's components, representing quantum states, cannot be completely determined from a finite set of probability measurements due to the probabilistic nature of quantum mechanics and the superposition principle, which implies that quantum states can exist in multiple states simultaneously until measured.

Question 20

The EPR argument assumes which of the following to conclude that quantum mechanics is incomplete?

Accepted Answer

The EPR argument, formulated by Einstein, Podolsky, and Rosen, assumes both that quantons (quantum particles) must have objectively real properties and that superluminal (faster than light) communication is impossible to conclude that quantum mechanics is incomplete. This argument is based on the idea that if quantum mechanics were complete, it would violate either the principle of locality (implying superluminal communication) or the principle of realism (the existence of objectively real properties independent of observation), leading to the conclusion that an additional, hidden variable theory is necessary.

Quiz 5: Matter Behaves Like Waves Quantum Physics

The point toward which compasses on the earth's surface point is a magnetic south pole.

Imagine a small magnet (with its north pole vertically upward) passing near the north pole of an external magnet that is below the small magnet. In what direction does the net force acting on the magnet point?

Imagine a small magnet with its north pole vertically upward passing near the south pole of an external magnet that is above the small magnet. In what direction does the net force acting on the magnet point?

It is possible with appropriately shaped external magnetic poles to create a situation where the effect of those poles does not vary with position along the SG axis. Imagine a small magnet placed in such a situation. What is the direction of the net force on the small magnet?

The direction of the net force on a small magnet will be the same if the SG axis is reversed and the effect of the external magnet decreases in the axis direction instead of increasing.

A muon is exactly like an electron (including having $|\vec{s}|=\frac{1}{2} \hbar$ ) except it is 207 times as massive. The classical model of spin would imply that a muon rotates

Which of the following is a valid spin state $q$ -vector? (If you are using the letters on the back cover, you can indicate more than one choice by pointing to several letters.)

Consider a set of electrons with an initial spin state $|\psi\rangle=\left[\begin{array}{l}0 \\1\end{array}\right]$ If we send these electrons into an SGx device, what is the probability a given electron will be determined to have its spin anti aligned with the $+x$ direction?

Imagine that an electron with an initial spin state $|\psi\rangle=\left[\begin{array}{l}\sqrt{1 / 2} \\\sqrt{1 / 2}\end{array}\right]$ Goes into an SGz device and comes out the - channel of that device. The electron's spin state is now

Imagine that an electron with an initial spin state $|\psi\rangle=\left[\begin{array}{c}\frac{3}{5} \\-\frac{4}{5}\end{array}\right]$ Goes into an SGx device and comes out the - channel of that device. The electron's spin state is now

Consider the following quantum state vector: $|\psi\rangle=\left[\begin{array}{c}\frac{3}{5} \\-\frac{4}{5}\end{array}\right]$ Which of the following $q$ -vectors is physically equivalent to the vector $|\psi\rangle$ ?

Suppose that a quanton's energy is zero, irrespective of its spin orientation. Suppose further that we prepare this quanton in an arbitrary spin state $|\psi(0)\rangle$ . The probability of any possible experimental outcome for any spin observable will then be independent of time.

We can completely determine a $q$ -vector's components from an appropriate set of probability measurements.

The EPR argument assumes which of the following to conclude that quantum mechanics is incomplete?

Quiz 5: Matter Behaves Like Waves Quantum Physics

The point toward which compasses on the earth's surface point is a magnetic south pole.

Imagine a small magnet (with its north pole vertically upward) passing near the north pole of an external magnet that is below the small magnet. In what direction does the net force acting on the magnet point?

Imagine a small magnet with its north pole vertically upward passing near the south pole of an external magnet that is above the small magnet. In what direction does the net force acting on the magnet point?

It is possible with appropriately shaped external magnetic poles to create a situation where the effect of those poles does not vary with position along the SG axis. Imagine a small magnet placed in such a situation. What is the direction of the net force on the small magnet?

The direction of the net force on a small magnet will be the same if the SG axis is reversed and the effect of the external magnet decreases in the axis direction instead of increasing.

A muon is exactly like an electron (including having ∣s⃗∣=12ℏ|\vec{s}|=\frac{1}{2} \hbar∣s∣=21​ℏ ) except it is 207 times as massive. The classical model of spin would imply that a muon rotates

The drawing below shows a sequence of Stern-Gerlach devices. By analogy to the cases discussed in the chapter, what do you think are the probabilities that an electron entering the last device will come out of that device's plus and minus channels, respectively?

The drawing below shows a sequence of Stern-Gerlach devices. By analogy to the cases discussed in the chapter, what do you think are the probabilities that an electron entering the last device will come out of that device's plus and minus channels, respectively?

Figure Q6.15 below shows a sequence of Stern-Gerlach devices. By analogy to the cases discussed in the chapter, what do you think are the probabilities that an electron entering the last device will come out of that device's plus and minus channels, respectively?

Which of the following is a valid spin state qqq -vector? (If you are using the letters on the back cover, you can indicate more than one choice by pointing to several letters.)

Imagine that an electron with an initial spin state ∣ψ⟩=[1/21/2]|\psi\rangle=\left[\begin{array}{l}\sqrt{1 / 2} \\\sqrt{1 / 2}\end{array}\right]∣ψ⟩=[1/2​1/2​​] Goes into an SGz device and comes out the - channel of that device. The electron's spin state is now

Imagine that an electron with an initial spin state ∣ψ⟩=[35−45]|\psi\rangle=\left[\begin{array}{c}\frac{3}{5} \\-\frac{4}{5}\end{array}\right]∣ψ⟩=[53​−54​​] Goes into an SGx device and comes out the - channel of that device. The electron's spin state is now

Consider the sequence of SG devices shown in figure Q7.7. Which of the expressions below gives the proper quantum amplitude that an electron emerging from the first SG device leaves via the - channel of the final device? (Do not assume that the inner product is commutative.) Figure 07.7

Consider the following quantum state vector: ∣ψ⟩=[35−45]|\psi\rangle=\left[\begin{array}{c}\frac{3}{5} \\-\frac{4}{5}\end{array}\right]∣ψ⟩=[53​−54​​] Which of the following qqq -vectors is physically equivalent to the vector ∣ψ⟩|\psi\rangle∣ψ⟩ ?

We can completely determine a qqq -vector's components from an appropriate set of probability measurements.

The EPR argument assumes which of the following to conclude that quantum mechanics is incomplete?

A muon is exactly like an electron (including having $|\vec{s}|=\frac{1}{2} \hbar$ ) except it is 207 times as massive. The classical model of spin would imply that a muon rotates

Which of the following is a valid spin state $q$ -vector? (If you are using the letters on the back cover, you can indicate more than one choice by pointing to several letters.)

Imagine that an electron with an initial spin state $|\psi\rangle=\left[\begin{array}{l}\sqrt{1 / 2} \\\sqrt{1 / 2}\end{array}\right]$ Goes into an SGz device and comes out the - channel of that device. The electron's spin state is now

Imagine that an electron with an initial spin state $|\psi\rangle=\left[\begin{array}{c}\frac{3}{5} \\-\frac{4}{5}\end{array}\right]$ Goes into an SGx device and comes out the - channel of that device. The electron's spin state is now

Consider the following quantum state vector: $|\psi\rangle=\left[\begin{array}{c}\frac{3}{5} \\-\frac{4}{5}\end{array}\right]$ Which of the following $q$ -vectors is physically equivalent to the vector $|\psi\rangle$ ?

We can completely determine a $q$ -vector's components from an appropriate set of probability measurements.