please answer all the parts with complet solution Suppose the electron in a hydr

Question

please answer all the parts with complet solution

Suppose the electron in a hydrogen atom occupies the combined position and spin state Determine the normalization constant A. What values of total and z-component orbital angular momentum might be measured and with what probabilities? What values of total z-component spin angular momentum might be measured and with what probabilities? What values of z-component total angular momentum (combined spin and orbital) might be measured? What energies might you measure and with what probablitlies?

Explanation / Answer

since there is a 5 and - 12

<psi|psi> = 5^2 + 12^2

so A = 1/sqrt(5^2 + 12^2)

b) total = sqrt( l(l+1)) hbar
z = mhbar

so for first state total=sqrt(2*3)hbar = sqrt(6) hbar
z = 1 hbar
with prob = (5/sqrt(5^2 + 12^2))^2=0.1479

for second state
total = sqrt(3*4)hbar = sqrt(12) hbar
z =-2 hbar
with prob = (12/sqrt(5^2 + 12^2))^2=0.852

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