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## Main Question or Discussion Point

What is the precise definition of the bound state condition? Thanks in advance.

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What is the precise definition of the bound state condition? Thanks in advance.

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malawi_glenn

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E < 0 and that the wavefunction "decays" to 0 as r-> infty

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Disagree with you, though i'm not insisting. Consider a harmonic oscillator: all energies > 0, still bound states. Wave function should "decay" at infinity, but something must be said about when it decays: e.g. a moving Gaussian wave packet decays faster than an exponent, but does not correspond to a bound state.E < 0 and that the wavefunction "decays" to 0 as r-> infty

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alxm

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If it wasn't an infinite potential well, the particle could tunnel out sooner or later. So it wouldn't be bound then.

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Or am I missing the point, maybe?

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