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23 Nov 2019
<p>A one dimensional harmonic oscillator is changed by the addition of another force so that V= (b/x<sup>2</sup>) + ½ mω<sup>2</sup>x<sup>2</sup>. One resulting wave function is ψ= Ax^ne<sup>-ax^2</sup> and d<sup>2</sup>ψ/dx<sup>2</sup> =[n(n-1)/x<sup>2</sup>– 2a(2n+1) + 4a<sup>2</sup>x<sup>2</sup>]ψ. Evaluate a and find E in terms of b, h and ω.</p>
<p>A one dimensional harmonic oscillator is changed by the addition of another force so that V= (b/x<sup>2</sup>) + ½ mω<sup>2</sup>x<sup>2</sup>. One resulting wave function is ψ= Ax^ne<sup>-ax^2</sup> and d<sup>2</sup>ψ/dx<sup>2</sup> =[n(n-1)/x<sup>2</sup>– 2a(2n+1) + 4a<sup>2</sup>x<sup>2</sup>]ψ. Evaluate a and find E in terms of b, h and ω.</p>
