1. (a) [5 points] Describe the similarities and di↵erences between spin and orbital angular momentum. Include in your discussion at least the following concepts: classical equivalence of each,...

1 answer below »
File attached


1. (a) [5 points] Describe the similarities and di↵erences between spin and orbital angular momentum. Include in your discussion at least the following concepts: classical equivalence of each, eigenvalues and eigenstates, Hamiltonians. Use words, equations, and diagrams as needed. (b) [5 points] Give a complete explanation of the meaning of “CSCO,” and what it implies for the states of the quantum systems it represents. Justify your discussion with appropriate mathematics, and cite examples from class that are CSCOs, and also some that are not (and why they are or aren’t). 2. An electron in the hydrogen atom is in the superposition state of the 1s, 2s, and 2p orbitals, (r, ✓,�) = 1p 2 R10(r)Y00(✓,�) + 1 2 R20(r)Y00(✓,�) + 1 2 R21(r)Y1,�1(✓,�) where Ylm(✓,�) are the usual spherical harmonics, and Rnl is the radial function and 1s �! R10(r) = 2a�3/20 e�r/a0 2s �! R20(r) = (2a0)�3/2 ✓ 2� r a0 ◆ e�r/(2a0) 2p �! R21(r) = 1p 3 (2a0) �3/2 ✓ r a0 ◆ e�r/(2a0) . (a)[3 points] If the Lz angular momentum is measured, what results can be found and with what probabilities? Explain your reasoning. (b) [3 points] Show how you would calculate the probability of finding the elec- tron between a = a0 and a = 5a0, where a0 is the Bohr radius (but don’t do the calculation!). Be sure to explain all terms in your calculation and show all steps! (c) [4 points] How you would calculate the average radial position of the elec- tron in this state? Be sure to explain all terms in your calculation and show all steps. 3. For this problem, recall that |+iu = cos ✓ 2 ! e�i�/2|+i+ sin ✓ 2 ! e+i�/2|�i |�iu = � sin ✓ 2 ! e�i�/2|+i+ cos ✓ 2 ! e+i�/2|�i (a) [3 points] For what angles ✓,� are the states |±ix and |±iy recovered? Show your work. (b) [3 points] A particle is prepared in the state |�iu oriented at an unknown angle ✓ (with � = 0). If there is a 0.35 probability of measuring the state |+ix, determine the preperation angle ✓ of the original state. (c) [4 points] A particle is prepared in the state |+i. It passes through a Stern-Gerlach apparatus oriented in the û�direction (at angles ✓ and �), but whose action is unknown. That is, the interim state could be |+iu or |�iu with equal probability. Show that the probability of measuring the state |�i after the particle emerges from the SG device is P = 14 cos 2 ✓. [Hint: Recall your trig identities....]
Answered Same DayFeb 24, 2022

Answer To: 1. (a) [5 points] Describe the similarities and di↵erences between spin and orbital angular...

Dr Shweta answered on Feb 24 2022
104 Votes
Solutions
Answer:
SOLUTION.PDF

Answer To This Question Is Available To Download

Related Questions & Answers

More Questions »

Submit New Assignment

Copy and Paste Your Assignment Here