# Quantum Mechanics 1 | Week 9

Session: JAN-APR 2024

Course name: Quantum Mechanics I

#### 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

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

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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 by
Then the commutator [Pr, R] will be

a)-ih
b)-2ih
c) ih
d) 2ih

Q4.

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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)

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

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Q7.

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

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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

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

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