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Schrodinger by numerical integration

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Issue:

Science

 

Written by:

Diane B

 

Date added:

September 27, 2015

 

Level:

University

 

Grade:

A

 

No of pages / words:

3 / 715

 

Was viewed:

7981 times

 

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Essay content:

The idea is that once we have verified that our numerical approach works for this system it can be extended to work for any one dimensional potential that we want, even if the analytic solutions are not known. Introduction The time independent Schrodinger’s equation in one dimension is: \* MERGEFORMAT We are looking at the simple harmonic oscillator for which , where k is the spring constant...
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To make the equation easier to solve, we use non dimensional variable: and Therefore Equation (1) reduces to: \* MERGEFORMAT Analytic solutions exist for equation (2), that take the form: Where are Hermite polynomials for n positive integers and zero given by the relation: With corresponding eigenvalues: With this I could then write a program to show the analytic solution of this problem...
displayed 300 characters

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