Given a potential $V$, how does one compute how shallow the potential can be such that it allows at least one bound state?
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2For one and two dimension, it always have a bound state. For 3D, this is not true. See: http://physics.stackexchange.com/q/143630/ – an offer can't refuse Jan 22 '15 at 04:04
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The issue is covered in the article "finite potential well" – Sofia Jan 22 '15 at 10:23
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To reopen this post (v1) consider to be more specific. – Qmechanic Dec 28 '19 at 21:56