# Quantum Mechanics 1 | Week 12

**Session: JAN-APR 2024**

**Course name: Quantum Mechanics I**

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#### These are Quantum Mechanics 1 Week 12 Assignment Nptel Answers

#### Q1. You are familiar with the particle in a box with wavefunction

(z) = sin(a) Ψη(x) 2 a

where 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 are

a) 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.

Answer:

**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)**

**Answer: **

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**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

**Answer: **

**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) -Ae

^{KX}for x > a, Ae

^{KX}for x < a

b) Ae

^{-KX}for x > a, Ae

^{KX}for x < a

c) Ae

^{KX}for x > a, Ae

^{-KX}for x < a

d) Ae

^{-KX}for x > a, -Ae

^{KX}for x < a

**(Неге к = √-2m E/ħ and A is a positive constant.)**

**Answer: **

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**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

**Answer: **

**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

Answer:

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**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)**

Answer:

**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) sin^{2} at

b) cos² at

c) 1

d) 1/2 e^{-iat}

**Answer: **

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**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 otherwisewhere a is a real positive constant. The most probable value of p will be**

a) a

b) 2a

c) a/2

d) a

^{2}/2

**Answer: **

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

a) True

b) False

**Answer: **

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**These are Quantum Mechanics 1 Week 12 Assignment Nptel Answers**

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