# Quantum Mechanics 1 | Week 10

**Session: JAN-APR 2024**

**Course name: Quantum Mechanics I**

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#### These are Quantum Mechanics 1 Week 10 Assignment Nptel Answers

#### Q1. When a state vector transforms into another state vector by a unitary transformation, an operator A transforms as A’. If A is Hermitian, then A’ is anti-Hermitian.

a) True

b) False

**Answer: b) False**

**Q2. The wavefunction of an electron in a Hydrogen-like atom is (r) = Ce-r/a, where a = ao/Z and an is the Bohr radius. The normalization constant C is**

a) 1/√4πa3

b) 1/√2πa3

c) 1/√πa3

d) 1/√a3

**Answer: a) 1/√4πa3**

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**These are Quantum Mechanics 1 Week 10 Assignment Nptel Answers**

**Q3. The eigenstate of Jx with eigenvalue ħ/2 will be**

a) 1/√8(-√3 -1 1 √3)

b) 1/√8(1 √3 √3 1)

c) 1/√2(-√3 -1 1 √3)

d)1/√2(1 √3 -1 -√3)

**Answer: d)1/√2(1 √3 -1 -√3)**

**Q4. Consider an operator = i.Jx.Jy. The expectation value of this operator for j = m = 1/2 is**

a) 1/2h2

b) 1/4h2

c) -1/2h2

d) -1/4h2

**Answer: b) 1/4h2**

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**These are Quantum Mechanics 1 Week 10 Assignment Nptel Answers**

**Q5. If (r) and (r) are the eigenfunctions of the parity operator belonging to even and odd eigenstates respectively, then they are orthogonal.**

a) True

b) False

**Answer: a) True**

**Q6.**

**Answer: a)**

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**These are Quantum Mechanics 1 Week 10 Assignment Nptel Answers**

**Q7. Classically, the rotational energy of a molecule is given as 2π²Iv², where I is the moment of inertia of the molecule and v is the number of revolutions per second. Moving to Quantum Mechanics, if such a rigid diatomic molecule is in the state l = 2, then the number of revolutions per second will be**

a) √6h/πI

b) 6h/πI

c) 6h/2πI

d) √6h/2πI

**Answer: d) √6h/2πI**

**Q8. For a harmonic oscillator, the Hamiltonian in dimensionless units (m = h = w = 1) iswhere the creation and annihilation operators are defined as,The energy eigenfunction of a state isThe quantum number related to this state is**

a) n = 2

b) n = 3

c) n = 4

d) n = 5

**Answer: a) n = 2**

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**These are Quantum Mechanics 1 Week 10 Assignment Nptel Answers**

**Q9. If x’ and p’x are the coordinate and momentum after time reversal, then the fundamental commu- tation [x’, p] is-ih.**

a) True

b) False

**Answer: a) True**

**Q10. The value of (1.0) [J², J.] [1,0) is**

a) 0

b) h

c) -h

d) -h²

**Answer: a) 0**

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**These are Quantum Mechanics 1 Week 10 Assignment Nptel Answers**

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