. Consider the following argument: If we have an electron in a potential of width a, then the kinetic energy is, by the uncertainty principle, larger than ħ²/2ma². Thus to get a bound state, the potential energy must not only be negative, but it must also be larger in magnitude than h²/2md. On the other hand, we have shown that in one dimension there is always a bound state, no matter how small V is, provided it is negative. What is wrong with this argument?
. Consider the following argument: If we have an electron in a potential of width a, then the kinetic energy is, by the uncertainty principle, larger than ħ²/2ma². Thus to get a bound state, the potential energy must not only be negative, but it must also be larger in magnitude than h²/2md. On the other hand, we have shown that in one dimension there is always a bound state, no matter how small V is, provided it is negative. What is wrong with this argument?
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Transcribed Image Text:. Consider the following argument: If we have an electron in a potential of width a, then the kinetic
energy is, by the uncertainty principle, larger than ħ²/2ma². Thus to get a bound state, the potential
energy must not only be negative, but it must also be larger in magnitude than h²/2md. On the other
hand, we have shown that in one dimension there is always a bound state, no matter how small V
is, provided it is negative. What is wrong with this argument?
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