# first-order energy correction in case of 1-D delta-function

Not what you're looking for?

Recall that a 1-D delta-function potential well of the form V (x) =

−B delta(x) had exactly one bound state, with a double-tailed exponential wave function.

(a) Apply a harmonic oscillator perturbation of the form V ′(x) = (m omega^2 x^2)/2. Calculate the

ground-state energy for this perturbed system to first order.

(b) Imagine instead that the harmonic oscillator is the original unperturbed system, and

the delta-function potential is the perturbation. Calculate the ground state energy for

this system to first order.

(c) Do your results agree with each other? Discuss why or why not.

##### Purchase this Solution

##### Solution Summary

Problem here was to calculate first-order energy correction when we have 1-D delta-function potential well as unperturbed system and some form of harmonic oscillator as perturbation and vice versa, when we have ground state of harmonic oscillator as unperturbed system and delta-function potential as perturbation.

##### Solution Preview

Recall that a 1-D delta-function potential well of the form had exactly one bound state with a double-tailed exponential wave function.

(a) Apply a harmonic oscillator perturbation of the form Calculate the

ground-state energy for this perturbed system to first order.

(b) Imagine instead that the harmonic oscillator is the original unperturbed system, and

the delta-function potential is the perturbation. Calculate the ground state energy for

this system to first order.

(c) Do your results agree with each other? Discuss why or why not.

Solution.

1-D delta-function potential well is defined as and it is well known (see for example Ref. 1 and 2) that bound state wave function has next form:

,

where and ...

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Introduction to Nanotechnology/Nanomaterials

This quiz is for any area of science. Test yourself to see what knowledge of nanotechnology you have. This content will also make you familiar with basic concepts of nanotechnology.

##### Classical Mechanics

This quiz is designed to test and improve your knowledge on Classical Mechanics.

##### Intro to the Physics Waves

Some short-answer questions involving the basic vocabulary of string, sound, and water waves.

##### Variables in Science Experiments

How well do you understand variables? Test your knowledge of independent (manipulated), dependent (responding), and controlled variables with this 10 question quiz.

##### The Moon

Test your knowledge of moon phases and movement.