Consider a particle of mass m subject to an attractive delta potential V(x) = - Vod(x), where Vo> 0 (Vo has the dimensions of Energyx Distance). (a) In the case of negative energies, show that this particle has only one bound state; find the binding energy and the wave function. (b) Calculate the probability of finding the particle in the interval -a ≤x≤ a. (c) What is the probability that the particle remains bound when Vo is (1) halved suddenly, (ii) quadrupled suddenly? (d) Study the scattering case (i.e., E > 0) and calculate the reflection and transmission coefficients as a function of the wave number k.

Consider a particle of mass m subject to an attractive delta potential V(x) = - Vod(x), where Vo> 0 (Vo has the dimensions of Energyx Distance). (a) In the case of negative energies, show that this particle has only one bound state; find the binding energy and the wave function. (b) Calculate the probability of finding the particle in the interval -a ≤x≤ a. (c) What is the probability that the particle remains bound when Vo is (1) halved suddenly, (ii) quadrupled suddenly? (d) Study the scattering case (i.e., E > 0) and calculate the reflection and transmission coefficients as a function of the wave number k.

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

Section: Chapter Questions

Problem 38P

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Question

Consider a particle of mass m subject to an attractive delta potential V(x) = - Vod(x), where
Vo> 0 (Vo has the dimensions of Energyx Distance).
(a) In the case of negative energies, show that this particle has only one bound state; find
the binding energy and the wave function.
(b) Calculate the probability of finding the particle in the interval -a ≤ x ≤ a.
(c) What is the probability that the particle remains bound when Vo is (1) halved suddenly.
(ii) quadrupled suddenly?
(d) Study the scattering case (i.e., E > 0) and calculate the reflection and transmission
coefficients as a function of the wave number k.

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