# Quantum Mechanics 1 | Week 4

Session: JAN-APR 2024

Course name: Quantum Mechanics I

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

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.

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.)

Q6. Consider a three-dimensional vector space spanned by an orthonormal basis (1), (2), (3). Kets a) and 3) are given by
a) = 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)

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)

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