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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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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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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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) is
where the creation and annihilation operators are defined as,
The energy eigenfunction of a state is
The 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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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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