- #1
icelevistus
- 17
- 0
A particle is described by the wave function
\[CapitalPsi] (\[Rho], \[Phi]) =
AE^(-\[Rho]^2/2 \[CapitalDelta]^2) (Cos[\[Phi]])^2
Show
P (Subscript[l, z] = 0) = 2/3
P (Subscript[l, z] = 2 h) = 1/6
P (Subscript[l, z] = -2 h) = 1/6
I have already used
Subscript[\[CapitalPhi], m] (\[Phi]) = 1/Sqrt[2 \[Pi]] E^Im\[Phi]
as the problem suggests to express the cos^2 as PHI(sub m) states
I am simply brickwalled at how to calculate these probabilities. The only way I remember to calculate probabilities given a wavefunction is for position (probability of measuring the particle within a certain region). Or also, I remember how to find the probability of a wavefunction collapsing to a particular state if it is written as a linear combination of states. Can someone point me to the relevant equation or idea?
\[CapitalPsi] (\[Rho], \[Phi]) =
AE^(-\[Rho]^2/2 \[CapitalDelta]^2) (Cos[\[Phi]])^2
Show
P (Subscript[l, z] = 0) = 2/3
P (Subscript[l, z] = 2 h) = 1/6
P (Subscript[l, z] = -2 h) = 1/6
I have already used
Subscript[\[CapitalPhi], m] (\[Phi]) = 1/Sqrt[2 \[Pi]] E^Im\[Phi]
as the problem suggests to express the cos^2 as PHI(sub m) states
I am simply brickwalled at how to calculate these probabilities. The only way I remember to calculate probabilities given a wavefunction is for position (probability of measuring the particle within a certain region). Or also, I remember how to find the probability of a wavefunction collapsing to a particular state if it is written as a linear combination of states. Can someone point me to the relevant equation or idea?
