A quanton is moving in a classically allowed region. If the quanton would classically have at point $x_{A}$ twice the kinetic energy it would have at point $x_{B}$, how would the wavelengths of an energy eigen function of the quanton compare at these points?
A) $\lambda_{A}=2 \lambda_{B}$
B) $\lambda_{A}=\sqrt{2} \lambda_{B}$
C) $\lambda_{B}=\sqrt{2} \lambda_{A}$
D) $\lambda_{B}=2 \lambda_{A}$
E) $\lambda_{B}=4 \lambda_{A}$

Question

Quizplus · Accepted Answer

The wavelength of a quanton is inversely proportional to its momentum, which is related to the square root of its kinetic energy. If the kinetic energy at $x_{A}$ is twice that at $x_{B}$, the wavelength at $x_{B}$ will be $\sqrt{2}$ times the wavelength at $x_{A}$, as per the de Broglie relation $\lambda = \frac{h}{p}$, where $h$ is Planck's constant and $p$ is the momentum.

A Quanton Is Moving in a Classically Allowed Region xAx_{A}xA​ Twice the Kinetic Energy It Would Have at Point

A Quanton Is Moving in a Classically Allowed Region $x_{A}$ Twice the Kinetic Energy It Would Have at Point