Answered: For what time-intependent potential…

For what time-intependent potential energy function V(r) does Y satisfy the Schrödinger equation for a particle of mass m?

University Physics Volume 3

17th Edition

ISBN:9781938168185

Author:William Moebs, Jeff Sanny

Publisher:William Moebs, Jeff Sanny

Chapter7: Quantum Mechanics

Section: Chapter Questions

Problem 43P: A particle with mass m is described by the following wave function: (x)=Acoskx+Bsinkx, where A, B,...

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Question

1.
A particle of mass m is in the state
Y(r, t) = Ac 25
= Ac 25
where A and w are positive real constants and i= v-1.
For what time-intependent potential energy function V(x) does Y satisfy the Schrödinger equation
for a particle of mass m?
(Simply plug the Y you are given into the time-dependent Schrödinger equation:
h a?¥(x,t)
aY(x,t)
ih
at
+V(x)¥(x,t) ,
2m
take the space and time derivatives and solve for V(x).]

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