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Eigenvalue problem and plotting its eigenfunctions [duplicate]

How many different ways can one solve an eigenvalue problem and plot its corresponding eigenfunctions in Mathematica? For example for Harmonic Oscillator? Which one is the most accurate one? Thanks ...
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Where can I find examples of good Mathematica programming practice?

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I read here the discussion about how to solve a one-dimensional eigenvalue problem. I am wondering, how can one generalize these methods to two dimensions? For example, how to solve this equation: ...
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How to numerically solve the Schrödinger equation for Lennard-Jones potential?

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How to add AccuracyGoal and PrecisionGoal options in a numerical function?

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Numerical solution of Schrödinger equation

I want to solve the following differential equation numerically. The geometry of the problem is as shown below. Electron 1 is located on the inner ring of radius $R_1$ and electron 2 is located on the ...