# Quantum Mechanics 1 | Week 7

**Session: JAN-APR 2024**

**Course name: Quantum Mechanics I**

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#### These are Quantum Mechanics 1 Week 7 Assignment Nptel Answers

#### Q1.

**Answer: b)**

**Q2. The sum of two non-interacting angular momenta J₁ and J₂ is given by J = J₁ + J2. Then which of the following commutation relations are correct?**

a) [Jr, Jy] =-ih.Jz

b) [Jy, Jz]=-ihJ

c) [J2, J²] = 0

d) [J2, J2] = 0**(Here J² is the total angular momentum and Jr, Jy, J₂ are the x, y, z components of the angular momentum operator respectively.)**

**Answer: c), d)**

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**These are Quantum Mechanics 1 Week 7 Assignment Nptel Answers**

**Q3. Consider a wavefunction (r, 0, 0) = C1Wmhmr + C2n212m2 which is a combination of normal- ized stationary state Hydrogen-like wavefunctions nim. For to be normalized c₁ and c₂ must satisfy the condition |C1| ^{2}+ |C1|^{2} = 1.**

a) True

b) False

**Answer: b) False**

**Q4. At time t = 0, the wavefunction of the Hydrogen atom is(r, 0) = 1 √10 (22/100+210 + √2211 + √3/21,-1)where the subscripts are the values of the quantum numbers n, l, m. The expectation value of the energy of the system is**

a) (E) = 1/10(2E1+ 4E2)

b) (E) = 1/10(2E1+ 6E2)

c) (E) = 1/10(4E1 – 6E2)

d) (E) = 1/10(4E₁ + 6E2)

**where E1, E2 are the energies of the first and second excited states respectively.**

**Answer: d) (E) = 1/10(4E₁ + 6E2)**

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**These are Quantum Mechanics 1 Week 7 Assignment Nptel Answers**

**Q5. The kets j, m) are the simultaneous eigenkets of total angular momentum operator J2 and its z component J₂ with eigenvalues j(j + 1)ħ² and mh respectively. Then J+j, m) and J_j, m) are also eigenkets of J2 with same eigenvalue.**

a) True

b) False

**Answer: a) True**

**Q6. One real operator A satisfies the equation A2-5A +6 = 0. Is A an observable?**

a) Yes

b) No

**Answer: a) Yes**

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**These are Quantum Mechanics 1 Week 7 Assignment Nptel Answers**

**Q7. Using the concept of parity, find out which of the following integrals are non-zero.**

a) (2s|x|2py)

b) (2s|x2|2px)

c) (2px|x2|2px)

d) (2p|x|3d)**Here the functions in the integrals are Hydrogen-like wavefunctions.**

**Answer: a), c), d)**

**Q8.**

Answer: 0.6

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**These are Quantum Mechanics 1 Week 7 Assignment Nptel Answers**

**Q9. Consider a system of two non-interacting identical particles of mass m confined in a two-dimensional box of sides a. The energy of the system in the state 2,2(x1, y1) 1,4 (x2, y2) will be N²pi²h²/2ma², where N = ___________.**

Answer: 5

**Q10.**

**Answer: d)**

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**These are Quantum Mechanics 1 Week 7 Assignment Nptel Answers**

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