# Quantum Mechanics 1 | Week 9

**Session: JAN-APR 2024**

**Course name: Quantum Mechanics I**

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#### These are Quantum Mechanics 1 Week 9 Assignment Nptel Answers

#### Q1. Yim (theta,fi) will be a simultaneous eigenstates of

(a) Lx, Ly, Lz

(b) L2, Lx, Lx

(c) Lx, Ly, L2

(d) Lz, L2

**Answer: (d) Lz, L2**

**Q2. For a spinless particle moving in a potential V(r), the time reversal operator T commutes with the Hamiltonian.**

a) True

b) False

**Answer: a) True**

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**These are Quantum Mechanics 1 Week 9 Assignment Nptel Answers**

**Q3. Consider an operator P, associated with the radial component of the momentum p, and an oper- ator R associated with radial coordinate r. Their actions on a radial wavefunction (r) are given byThen the commutator [Pr, R] will be**

a)-ih

b)-2ih

c) ih

d) 2ih

**Answer: a)-ih**

**Q4.**

**Answer: a)**

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**These are Quantum Mechanics 1 Week 9 Assignment Nptel Answers**

**Q5. Consider a coherent state that is an eigenstate of annihilation operator such that ala) = ala). The probability P(n) of finding the state (a) in the number state In = 2) is exp(a/2), where q= _________. (Answer should be an integer)**

Answer: 2

**Q6. Using the properties of the Pauli matrices, the expression exp to be turns out to be**

a) equal to σz + pi

b) equal to σy – iσz

c) proportional to σx.

d) proportional to σz

**Answer: d) proportional to σz**

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**These are Quantum Mechanics 1 Week 9 Assignment Nptel Answers**

**Q7.**

**Answer: a)**

**Q8. Consider a particle in a Coulomb potential in three-dimensional space. In Heisenberg’s picture, if (L) = 0, where L. is the z-component of angular momentum operator. This would imply that H, L, form share same eigenbasis.**

a) True

b) False

**Answer: a) True**

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**These are Quantum Mechanics 1 Week 9 Assignment Nptel Answers**

**Q9. Consider an electron subjected to a uniform magnetic field B = Bê, with the vector potential A and the Hamiltonian of the electron is H = (I+II+p²), where II₁=p. The 2m C commutator bracket [II,II] is**

а) іћ Пу

b) 2іћ Пу

c) iћ Пx

d) 2iћ Пx

**Answer: b) 2іћ Пу**

**Q10. The Hamiltonian of a spin-3/2 particle is H =(S+S-S) S, where c and d are constants. The energy levels for such a particle with magnetic quantum number m = 1/2 is**

a) 13/4C+ d/2

b) 13/4C – d/2

c) 13/2C – d/2

d) 13/2C + d/2

**Answer: b) 13/4C – d/2**

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**These are Quantum Mechanics 1 Week 9 Assignment Nptel Answers**

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