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So I read that the delta function potential well has one and only one bound state. This seems to give a precise momentum and position as the bound state has a definite energy and the particle must be in the well. This seems to be a violation of the HUP. Is the physical impossibility of creating a true delta function potential the savior here?

Ahh I forgot about the exponential fall off outside the well. So I suppose there is still some uncertainty in position, though is it enough to counter a zero uncertainty in momentum? For that matter the regular finite potential well has bound states that have exact energies (and therefore momenta) and yet the uncertainty in position seems to not be big enough to satisfy the HUP?

Are these finite potential well bound states (stationary states) not realizable by particles. Can particles only be described by wave packets?

Ahh I forgot about the exponential fall off outside the well. So I suppose there is still some uncertainty in position, though is it enough to counter a zero uncertainty in momentum? For that matter the regular finite potential well has bound states that have exact energies (and therefore momenta) and yet the uncertainty in position seems to not be big enough to satisfy the HUP?

Are these finite potential well bound states (stationary states) not realizable by particles. Can particles only be described by wave packets?

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