Consider a quanton in a box. How does the wavelength $\lambda$ of an energy eigen function in this case depend on the energy $E$ corresponding to that eigen function?
A) $\lambda \propto E$
B) $\lambda \propto \sqrt{E}$
C) $\lambda$ is independent of $E$.
D) $\lambda \propto 1 / \sqrt{E}$
E) $\lambda \propto 1 / E$

Question

Quizplus · Accepted Answer

The wavelength $\lambda$ of an energy eigenfunction for a particle in a box is inversely proportional to the square root of the energy $E$. This relationship comes from the de Broglie hypothesis, which relates the momentum $p$ of a particle to its wavelength $\lambda$ through the equation $\lambda = h/p$, where $h$ is Planck's constant. The energy $E$ of a particle in a box is related to its momentum by the equation $E = p^2/(2m)$, where $m$ is the mass of the particle. Combining these equations shows that $\lambda$ is proportional to $1/\sqrt{E}$.

Consider a Quanton in a Box λ\lambdaλ Of an Energy Eigen Function in This Case Depend on \lambda

Consider a Quanton in a Box $\lambda$ Of an Energy Eigen Function in This Case Depend on \lambda