# Quantum Mechanics 1 | Week 12

Session: JAN-APR 2024

Course name: Quantum Mechanics I

#### Q1. You are familiar with the particle in a box with wavefunction(z) = sin(a) Ψη(x) 2 awhere a represents the side of the box and the potential is zero for (0 ≤ x ≤ a) and infinite elsewhere. The statements which best describe such a particle area) Each function (2) has n – 1 nodes.b) The wavefunctions corresponding to different energy levels are orthogonal.c) Some energy levels are degenerate.d) The energy between adjacent levels is constant.

Q2. The wavefunction for a free particle of mass m is (x,t) = A exp i(kx), where A is the normalization constant. The probability current J will be
a) [hk/2m]|A|2
b) [hk2/m]|A|2
c) [hk/m]|A|2
d) [hk²/2m]|A|2
(Here k = √2mE/ћ)

These are Quantum Mechanics 1 Week 12 Assignment Nptel Answers

Q3. The function = sin(k₁x) sin(k₂y) sin(kaz) is an eigenfunction of Laplacian operator V2.
a) True
b) False

Q4. A particle moving in one dimension is confined by a double delta function potential,
V(x) = -98(х – а) – дб (х + а),
where g and a are positive constants. The general forms of bound state odd wave functions when energy E < 0 are

a) -AeKX for x > a, AeKX for x < a
b) Ae-KX for x > a, AeKX for x < a
c) AeKX for x > a, Ae-KX for x < a
d) Ae-KX for x > a, -AeKX for x < a
(Неге к = √-2m E/ħ and A is a positive constant.)

These are Quantum Mechanics 1 Week 12 Assignment Nptel Answers

Q5. A spin 1 particle is in the state |) = 1/√14(1 2 3i) in Sz basis. Then (Sx) will be
a) √2(1+3i)*h/7
b) √2ħ/7
c)2h/7
d) √2/7h

Q6. A spin-1/2 particle is in the state 1/√2(|+> +|->). Then, the expectation value of the operator i Sx Sy will be
a) 0
b) h²/4
c) h²/2
d) h²

These are Quantum Mechanics 1 Week 12 Assignment Nptel Answers

Q7. Consider a system of five non-interacting particles with identical spin that are in the same state ), confined to move in a one dimension infinite potential well of length L. The potential is V(x) = 0 for 0<x< Land V(x) = ∞ elsewhere. The ground state energy of the system is Nh/2mL2, where N is ________. (Answer should be an integer)

Q8. For the Hamiltonian H = a1 >< 2 + a/2 >< 1, obtain the state vector for t > 0. Then the corresponding probability for it to be in state (2) will be (Hint: Take h = 1)
a) sin2 at
b) cos² at
c) 1
d) 1/2 e-iat

These are Quantum Mechanics 1 Week 12 Assignment Nptel Answers

Q9. A wavefunction of a system in cylindrical coordinates is given as ψ(ρ, φ, 2) = Αe-p/a for |z| <1 and 0 otherwise
where a is a real positive constant. The most probable value of p will be

a) a
b) 2a
c) a/2
d) a2/2

Q10. If |x) and |fie) belong to the same vector space, then the outer product |fie) <| is another vector.
a) True
b) False