How many bound states are there

Outside the well, the potential is zero. Here, we will describe a few key aspects of the calculation, bypassing most of the details. For a fuller discussion of the transfer matrix method, refer to Appendix B. The choice of boundary conditions determines whether the solution we get is a bound state or free state. Furthermore, the wavefunction for a bound state can always be normalized:. For a free state, the situation is quite different.

The wavefunction does not vanish exponentially at infinity, but takes the form. The energy spectrum is shown on the left side. These results were computed using the transfer matrix method described in Appendix B. Many of the lessons drawn from the square well model can be generalized to more complicated potentials.

Energies and numbers of bound states in finite potential well Ask Question. Asked 8 years, 7 months ago. Active 1 year, 9 months ago. Viewed 19k times. Improve this question. Add a comment. Active Oldest Votes. Improve this answer.

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