Quantum Mechanics 1 | Week 3

Session: JAN-APR 2024

Course name: Quantum Mechanics I

Course Link: Click Here

For answers or latest updates join our telegram channel: Click here to join

These are Quantum Mechanics 1 Week 3 Assignment Nptel Answers

---

Q1. The commutator of two Hermitian operators is Hermitian.
a) True
b) False

Answer: b) False

---

Q2. Which of the following operators are Hermitian?
a) d/dx
b) i*d/dx
c) e^d/dx
d) e^id/dx

Answer: b), d)

---

Q3. Consider two operators A and B defined by, Αψ(x) = ψ(x) +x and Bψ(x) = (dψ/dx)+2ψ(x). Which of the following statements about their linearity is true?
a) A is linear, B is not linear
b) B is linear, A is not linear
c) both A and B are linear
d) both A and B are not linear

Answer: b) B is linear, A is not linear

---

For answers or latest updates join our telegram channel: Click here to join

These are Quantum Mechanics 1 Week 3 Assignment Nptel Answers

---

Q4. Which of the following statements about projection operators are true?
a) An operator P is said to be a projection operator if it is Hermitian and equal to its own square.
b) The operator |ψ><ψ| is a projection operator only when |ψ> is normalized.
c) Two projection operators are said to be orthogonal if their product is 0.
d) The product of any two projection operators is always a projection operator.

Answer: a), b), c)

---

Q5. Consider a ket |ψ> = (5i 2 -i) which is not normalized. It can be normalized by multiplying it with a factor of 1/√a, where a = _______. (Answer should be an integer)

Answer: 30

---

Q6. Consider a ket |ψ> = (-1+i 3 2+3i) and bra <ⲫ|= (6 -i 5). The value of <ψ|ⲫ) will be a-bi.
i) a = ________ (Answer should be an integer)
ii) b = _________ (Answer should be an integer)

Answer: 4,18

---

For answers or latest updates join our telegram channel: Click here to join

These are Quantum Mechanics 1 Week 3 Assignment Nptel Answers

---

Q7. The Hermitian adjoint of f(A) = (1 – 2iA +3A)(1 + iA – 24) is
a) (1-2iA†+ 3A†)(1 +2iA† – 2¹)
b) (1-iA† – 2A†)(1 +2iA† + 3¹)
c) (1 + 2iA – 3A)(1 -iA† + 2¹)
c) (1 – iA + 2A)(1 – 2iA† – 3¹)
(where the linear operator  ≠ †)

Answer: b) (1-iA† – 2A†)(1 +2iA† + 3¹)

---

Q8. Evaluate the commutator [x, [x, H]], where H is the Hamiltonian operator.
a) ħ²/m
b) -ħ²/m
c) ħ²/2m
d) -ħ²/2m

Answer: b) -ħ²/m

---

These are Quantum Mechanics 1 Week 3 Assignment Nptel Answers

---

Q9. Consider the states |ψ> = 3i|ⲫ1> – 7i|ⲫ2> and |x> = -|ⲫ1> + 2i|ⲫ2>, where |ⲫ1> and |ⲫ2> are orthonormal. Then <ψ+ x|ψ + x> is _________________. (Answer should be an integer)

Answer: 35

---

These are Quantum Mechanics 1 Week 3 Assignment Nptel Answers

---

Q10. Consider the states |ψ1> = 2i|ⲫ1> + |ⲫ2> + a|ⲫ3> + 2|ⲫ4> and |ψ2> = 2|ⲫ1> – 3|ⲫ2> + 3|ⲫ3> – |ⲫ4>, where |ⲫ1>, |ⲫ2>, |ⲫ3>, |ⲫ4> are orthonormal kets and a is a constant. The value of a so that |ψ1> and |ψ2> are orthogonal is
a) (7i-2)/3
b) (-7i+2)/3
c) (7i+2)/-3
d) (-6i-2)/3

Answer: b) (-7i+2)/3

---

For answers or latest updates join our telegram channel: Click here to join

These are Quantum Mechanics 1 Week 3 Assignment Nptel Answers

More Weeks of Quantum Mechanics I: Click here

More Nptel Courses: https://progiez.com/nptel-assignment-answers