# One-Dimensional Time-Independent Schrodinger

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4.15. A particle is moving in a simple harmonic oscillator potential V(x) = 1/2kx^2 for x>0, but with an infinite potential barrier at x=0 (the paddle ball potential). Calculate the allowed wave functions and corresponding energies.

4.16. A particle moves in one dimension in the potential V(x) Vo ln(x/xo) for x>0, where xo and Vo are constants witht he units of length and energy, respectively. There is an infinite potential barrier at x=0. The particle drops from the first excited state with energy E1 into the ground state with energy Eo by emitting a photon with energy E1-E0. Show that the frequency of the photon emitted by this particle is independent of the mass of the particle.

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##### Solution Summary

This solution shows step-by-step calculations and explanations to determine the eigenfunctions and finally the frequency of the photon emitted by this particle that is independent of the mass of the particle using the Schrodinger equation.

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The explanations are in the attached pdf file.

The quoted formulae should ...

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