Consider a particle without spin given by the wave function V = y (x + y + 2z) e-ar, Where :r = Vx² + y² + z² with Y and a real constants. a) Calculate the total angular momentum of the particle b) What is the expectation value of the z component of angular momentum? c) If the z component of angular momentum is measured, what is the probability that the result is h ?
Consider a particle without spin given by the wave function V = y (x + y + 2z) e-ar, Where :r = Vx² + y² + z² with Y and a real constants. a) Calculate the total angular momentum of the particle b) What is the expectation value of the z component of angular momentum? c) If the z component of angular momentum is measured, what is the probability that the result is h ?
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Transcribed Image Text:Consider a particle without spin given by the wave function
V = y (x + y+2z) e-ar,
Where :r = Vx² + y² + z² with Y and a real constants.
a) Calculate the total angular momentum of the particle
b) What is the expectation value of the z component of angular momentum?
c) If the z component of angular momentum is measured, what is the probability that the result is h ?
d) What is the probability of finding the particle in 0. , 0 and the solid angle d2? Where the angles 0. Y O
are the usual spherical coordinates.
Hint: Consider the following spherical harmonics
3
3
1
YO
Y° = /
cos 0,
47
Y =
sin de±iø
87
4T
15
sin 0 cos de±io.
87
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