Consider a particle with the following wave-function: ,x<0 2 y(x) ={A| L ,0L and L and A are constants. (a) What is the normalization constant A (in terms of L)? (b) What is (in terms of L)? ? (ie, ) (c) What is the probability that the particle will be found within x = 0 and L/2?

Consider a particle with the following wave-function: ,x<0 2 y(x) ={A| L ,0L and L and A are constants. (a) What is the normalization constant A (in terms of L)? (b) What is (in terms of L)? ? (ie, ) (c) What is the probability that the particle will be found within x = 0 and L/2?

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

Chapter8: Quantum Mechanics In Three Dimensions

Section: Chapter Questions

Problem 7P

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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.

Question

Consider a particle with the following wave-function:
,x<0
y(x) ={A-
L
,0<x<L
,x>L
and L and A are constants.
(a) What is the normalization constant A (in terms of L)?
(b) What is <x> (in terms of L)? ? (ie, <r>)
(c) What is the probability that the particle will be found within x=0 and L/2?

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