How to Solve the Schrödinger Equation for a 3D Isotropic Harmonic Oscillator?

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Homework Help Overview

The discussion revolves around solving the Schrödinger equation for a three-dimensional isotropic harmonic oscillator, specifically using separation of variables in spherical polar coordinates.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the initial steps required to tackle the problem, including finding the Laplacian in spherical coordinates and expanding the Schrödinger equation. There is also mention of the potential energy expression relevant to harmonic oscillators.

Discussion Status

Some participants have suggested starting points for the solution, while others have referenced external resources. There appears to be a mix of attempts and suggestions, but no consensus on a specific approach has been reached.

Contextual Notes

Participants note that the problem is commonly discussed in various textbooks, indicating a shared understanding of its relevance in the field. There is also a hint of frustration regarding the search for straightforward solutions to standard physics problems.

eman2009
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Homework Statement




solve the schrodenger equation for the3-D isotropic harmonic oscilator by sepration of varibals in sphericalpolar coordenates.

Homework Equations




The Attempt at a Solution

 
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ok, attempt to solution?

(there is a discussion on this in many textbooks, such as the nuclear shell model by Heyde)
 
for a start, find out what the laplacian is in spherical coords and expand the shrodinger equation. from there you need to separate your variables. remember also that your potential energy is a certain expression if you dealing with a harmonic oscillator.
 

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