Question

why zero point energy of particle on a ring is zero

Answer 1

Hi buddy!

In the standard particle in an infinite ring, there is no potential in the ring. This means the total energy is just the kinetic energy, so E=0 corresponds to zero kinetic energy and thus corresponds to zero momentum. If we try to calculate the uncertainty in the momentum using a wavefunction that is a constant zero everywhere, you will most likely end up with zero, and this clearly defies the uncertainty principle.

You'll get the same result for the position. So n=0 isn't considered a physical state. Having a wavefunction which is a constant zero is sufficient to come to that conclusion. it is pretty common to say the n=0 state has no particle in it. The postulates in quantum mechanics are chosen not just because they are mathematically consistent but also because they 'make sense'.

Thanks and hope this helps!

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