Quantum-Mechanical Average Value of the Potential Energy

J Summary of Solution of Harmonic-Oscillator Schrodinger Equation [Pg.83]

The detailed solution is so long that the reader may have lost the broad outline. [Pg.83]

Determine the asymptotic behavior of the Schrodinger equation and of xj/. This produces a gaussian factor exp(-y /2) times a function of y, f y). [Pg.83]

Represent /(y) as a power series in y, and find a recursion relation for the coefficients in the series. The symmetries of the wavefunctions are linked to the symmetries of the series. [Pg.83]

Force the power series to be finite (i.e., polynomials) so as not to spoil the asymptotic behavior of the wavefunctions. This leads to a relation between a and that produces uniformly spaced, quantized energy levels. [Pg.83]

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