The wave function of a particle in two dimensions in plane polar coordinates is given by: T Y(r,0) = A.r.sinoexp 2a0. where A and ao are positive real constants. 1. Find the constant A using the normalization condition in the form SIY(r.0)|²rdrd0 = 1 2. Calculate the expectation values of r, and ². 3. Assuming that the momentum operator in plane polar coordinate is giving in the form p=calculate the expectation values of p and p². 4. Find the standard deviations of r and p and show that their product is consistent with the Heisenberg uncertainty principle.
The wave function of a particle in two dimensions in plane polar coordinates is given by: T Y(r,0) = A.r.sinoexp 2a0. where A and ao are positive real constants. 1. Find the constant A using the normalization condition in the form SIY(r.0)|²rdrd0 = 1 2. Calculate the expectation values of r, and ². 3. Assuming that the momentum operator in plane polar coordinate is giving in the form p=calculate the expectation values of p and p². 4. Find the standard deviations of r and p and show that their product is consistent with the Heisenberg uncertainty principle.
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Transcribed Image Text:The wave function of a particle in two dimensions in plane polar coordinates is given by:
T
¥(r,0) = A. r. sin0exp[-
where A and ao are positive real constants.
1. Find the constant A A using the normalization condition in the form
SS |¥(r,0)|²rdrd0 = 1
2. Calculate the expectation values of r, and ².
3. Assuming that the momentum operator in plane polar coordinate is giving in the form
ħa
p = calculate the expectation values of p and p².
1 Ər'
4. Find the standard deviations of r and p and show that their product is consistent with
the Heisenberg uncertainty principle.
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