A particle, which is initially (t = 0) in the ground state of an infinite, one-dimensional potential box with walls at x = 0 and x = a, is subjected for 0 < t s∞, to a perturbation V (t) = x*e. Calculate to first order the probability of finding the particle in its first excited state for t>0.

A particle, which is initially (t = 0) in the ground state of an infinite, one-dimensional potential box with walls at x = 0 and x = a, is subjected for 0 < t s∞, to a perturbation V (t) = x*e. Calculate to first order the probability of finding the particle in its first excited state for t>0.

Modern Physics

3rd Edition

ISBN:9781111794378

Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Chapter6: Quantum Mechanics In One Dimension

Section6.4: The Particle In A Box

Problem 1E

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Concept explainers

Connection formulae for WKB approximation

In quantum mechanics, Schrödinger’s equation for certain systems with varying parameters cannot be solved directly. In such a case, an approximation method is used to obtain the approximate solution. WKB method is a special technique used to obtain the approximate solution for Schrödinger’s time-independent equation. In general, the WKB method is used to solve linear differential equations with varying coefficients. This method is called semiclassical approximation in quantum mechanics.

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A particle, which is initially (t = 0) in the ground state of an infinite, one-dimensional
potential box with walls at x = 0 and x = a, is subjected for 0 <t < ∞, to a perturbation
V (t) = x'e. Calculate to first order the probability of finding the particle in its first excited
state for t >0.

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