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