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Is there a general method for determining the number of bound states admitted by a potential in the Schrodinger equation?

Certainly the number of dimensions must factor in somehow: the delta potential for example is pathological in 3D, whereas it admits a single bound state in 1D.

Thanks!

anon01
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  • Possible duplicate of: http://physics.stackexchange.com/q/210272/ – Gert Oct 12 '15 at 16:44
  • @Gert this is in NO WAY a duplicate of that question, but is tangentially related. Thanks for the heads up. – anon01 Oct 12 '15 at 17:03
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    Formula (1) in my Phys.SE answer here is a semi-classical formula for the number $N(E)$ of bound states below energy-level $E$ in 1D. – Qmechanic Oct 12 '15 at 18:25

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