Consider a highly excited He atom. One electron is in a state with n1
= 4, l1 = 3 and the other in a state with n2 = 5, l2 = 4
(a) Find the possible values of l (total orbital angular momentum
quantum number) for the system.
(b) Find the possible values of s (total spin angular momentum quantum number)
for the system.
(c) Find the possible values of j (total angular momentum quantum number)
for the system.
(d) How many distinct angular momentum states with j = 1 are there?
(a) Write down Maxwell's equations for a conducting medium with conductivity σ,
permittivity ε0 and permeability μ0.
(b) A plane wave of low frequency ω << σ/ε0 is propagating in the
z-direction inside the conducting medium.
Let E = E0exp(i(kz - ωt)),
B = B0exp(i(kz
- ωt)), where E0, B0, and k are complex.
Use Maxwell's equations to show that k = k1 + ik2, k1
≈ k2 ≈ (μ0ωσ/2)½.
Calculate the ratio of the complex amplitude of the two fields, E0/B0
(magnitude and phase).
(c) Calculate the energy flux (time averaged Poynting vector) in the
conducting medium.
Consider a two-level system |Φa>, |Φb> with <Φi|Φj>
= δij. Show that an "entangled", two-particle state of the form
α|Φa(1)>|Φb(2)> + β|Φb(1)>|Φa(2)>,
α, β ≠ 0,
CANNOT be written as a product state |ψr(1)>|ψs(2)> for
any one particle states |ψr> and |ψs>.
A beam of monochromatic light of wavelength λ in vacuum is incident normally on a nonmagnetic dielectric film of refractive index n and thickness d. Calculate the fraction of the incident energy that is reflected.