# Quantum Mechanics 1 | Week 6

**Session: JAN-APR 2024**

**Course name: Quantum Mechanics I**

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#### These are Quantum Mechanics 1 Week 6 Assignment Nptel Answers

#### Q1. Consider a system whose Hamiltonian is given by H = (01) (2+2)(011), where a is real number having dimensions of energy and 1), 2) are normalized eigenstates of a Hermitian operator A that has no degenerte eigenvalues. Is H a projection operator?

a) Yes

b) No

**Answer: b) No**

**Common data for Q2 & Q3**

**Consider a one-dimensional harmonic oscillator with Hamiltonian H = p2 +mw²x2. The position and momentum operators in the Heisenberg picture for this harmonic oscillator are respectively given asXH(t) = X cos(wt) + P sin(wt) mwPH(t) = P cos(wt) – mw x sin(wt).Then the commutators**

**Q2. [PH (t1), PH (t2)] will be**

a) iħmw sin[w(t1-t2)]

b) -ih/mw sin[w(t1 t2)]

c) -ihmw cos[w(t₁-t2)]

d) -ih/mw cos[w(t1 t2)]

**Answer: a) iħmw sin[w(t1-t2)]**

**Q3. [XH(1), XH (2)] will be**

a) -ihmw sin[w(t₁-t2)]

b) -ih/mw sin[w(t1 – t2)]

c) -ihmw cos[w(t1-t2)]

d) -ih/mw cos[w(t1 – t2)]

**Answer: b) -ih/mw sin[w(t1 – t2)]**

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**These are Quantum Mechanics 1 Week 6 Assignment Nptel Answers**

**Q4. Consider a system of two spin-half particles, in a state with total spin quantum number S = 0. If the spin Hamiltonian is H = AS1.S2, where A is a positive constant and S1, S2 are spin angular momentum operators, then the eigenvalue of the Hamiltonian will be**

a)-3/2Ah²

b) 3/2Ah²

c) -3/4Ah²

d) 3/4Ah²

**Answer: c) -3/4Ah²**

**Q5.**

**Answer: a), d)**

**Q6. For the case, n = 2,1 = 1, m₁ = 0, the value of r at which the radial probability density of the hydrogen atom reaches its maximum is ___________ a _{0}. (Answer should be an integer)**

Answer: 4

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**These are Quantum Mechanics 1 Week 6 Assignment Nptel Answers**

**Q7. The Hamiltonian of a system is given by H(t) = + V(R(t)). The Heisenberg equation of 2m motion for the position operator R(t) in the Heisenberg picture for this system can be written as**

a) dR/dt = P2/2m

b) dR/dt = P/m

c) dR/dt = P/2m

d) dR/dt = P/2ihm

**Answer: b) dR/dt = P/m**

**Q8. The first excited state of Hydrogen atom is ________ fold degenerate when we take into account the spin of the electron. (Answer should be an integer)**

Answer: 8

**These are Quantum Mechanics 1 Week 6 Assignment Nptel Answers**

Q9.

**Answer: c)**

**These are Quantum Mechanics 1 Week 6 Assignment Nptel Answers**

**Q10. The expectation value of a physical observable in Schrodinger’s representation (Os) is the same as its expectation value in Heisenberg’s representation (н).**

a) True

b) False

**Answer: a) True**

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**These are Quantum Mechanics 1 Week 6 Assignment Nptel Answers**

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