Question

Find the energy eigenvalues of a particle confined by a potential of the following form: +oo, V(r)= { }mu22, if 2 0. if r0 <Hint: Use the fact that we already know the energy eigenvalues and eigenfunctions of the Schrödi- inger equation in the quadr

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Answer #1

We already know the solutions for quadratic potential.

In this particular problems only those states will be allowed which have their wave function continuous at the boundary.

Since wave function is essentially zero in left half so only those wave functions are allowed which vanish as they approach to Y-axis(fig (b)).

1/mwssez 0 figca) tan) K Allowed na3 AA n=2 t no 2 - - not allowed Allowed n= n =0 MOT allowed ли tig (b) so allowed raluss d

I will attach the solution.

Let me know if that helps or if you have further queries(related to the same question).
regards,

note: this question should be asked in advanced physics.

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