# Quantum Mechanics 1 | Week 4

**Session: JAN-APR 2024**

**Course name: Quantum Mechanics I**

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#### These are Quantum Mechanics 1 Week 4 Assignment Nptel Answers

#### Q1. If operator A is Hermitian, then the operator B = iA is Hermitian.

a) True

b) False

**Answer: b) False**

**Q2. Which of the following statements about parity operator are correct?**

a) Parity operator Pis anti-Hermitian.

b) P is unitary.

c) P2 is equal to unity operator Î.

d) The eigen values of Pare +1 or -1.

**Answer: b), c), d)**

**Q3. Consider the states ) = 9i|61) +202) and (x) = -1)+12), where the vectors (1) and 2) form a complete and orthonormal basis. Then Tr()(x) is a/√b, where**

i) a = ________ (Answer should be an integer)

ii) b = ________ (Answer should be an integer)

**Answer: 7,2**

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**These are Quantum Mechanics 1 Week 4 Assignment Nptel Answers**

**Q4. By evaluating the commutator [A, [B, C]D] we get**

a) CBDA-BCDA+ABCD-ACBD

b) ABCD-CDBA+BACD – DCBA

c) CBDA + BCDA-ABCD+ACBD

d) ABCD-BCDA + DCBA- DABC**Here A, B, C, D are linear operators.**

**Answer: a) CBDA-BCDA+ABCD-ACBD**

**Q5. Given that, V)=(4+3i)|V₁)-4 exp(-3/2)|V₂), where V₁) and V₂) are orthonormal pair of kets. Then the norm of V) is √a, where, a = _________. (Answer should be an integer.)**

Answer: 41

**Q6. Consider a three-dimensional vector space spanned by an orthonormal basis (1), (2), (3). Kets a) and 3) are given bya) = 1)-22)-3), 3) = 1) + 2/3)Then the inner product (aẞ) = a + bi, where**

i) a = _______ (Answer should be an integer)

ii) b = _______(Answer should be an integer)

**Answer: 1,2**

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**These are Quantum Mechanics 1 Week 4 Assignment Nptel Answers**

**Q7. Consider an unnormalized state which is given in terms of three orthonormal vectors as follows.where) are eigenstates of an operator B such that Bon) = n2n) with n = 1, 2, 3. Then the expectation value of B for the state would be a/b where**

i) a = _______ (Answer should be an integer)

ii) b = _______ (Answer should be an integer)

**Answer: 11,4**

**Q8. Consider a pair of orthogonal kets V₁) and V₂). The dual of the ket (V) (53) Vi) + 3exp(-13/2)|₂), will be**

a) (5+3i) V₁) + 3exp(3/2)|V₂)

b) (5+3i) (V₁ + 3exp(3/2) (V2

c) (53) (V₁ + 3exp(-13/2) (2

d) (5+3i) (Vi 3exp(23/2) (V2

**Answer: b) (5+3i) (V₁ + 3exp(3/2) (V2**

**These are Quantum Mechanics 1 Week 4 Assignment Nptel Answers**

**Q9. Consider an operator B = 1) (2 where (1) and (2) are orthonormal. Then the correct statement about B² and BB is**

a) B2 is 1 and BB is 0.

b) B² is 1 and BB is a projection operator.

c) B2 is 0 and BB is a projection operator.

d) B² is a projection operator and BB is 0.

**Answer: c) B2 is 0 and BB is a projection operator.**

**These are Quantum Mechanics 1 Week 4 Assignment Nptel Answers**

**Q10. The parity of both the position operator R and momentum operator Pare odd.**

a) True

b) False

**Answer: a) True**

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**These are Quantum Mechanics 1 Week 4 Assignment Nptel Answers**

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