# Quantum Mechanics 1 | Week 1

**Session: JAN-APR 2024**

**Course name: Quantum Mechanics I**

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

**Q1. The energy eigenvalue and the corresponding eigenfunction for a particle of mass m in a one-dimensional potential V(x) are,**

E=0, (x)=A/(x^2+a^2)

where A is a positive constant. The form of potential V(x) is

a) h2(3x^2-a^2)/m(x^2+a^2)^2

b) h2(x^2-a^2)/2m(x^2+a^2)^2

c) h2(3x^2-a^2)/m(x^2+a^2)^3

d) h2(x^2-a^2)/2m(x^2+a^2)^3

E=0, (x)=A/(x^2+a^2)

where A is a positive constant. The form of potential V(x) is

**Answer: a) h2(3x^2-a^2)/m(x^2+a^2)^2**

**Q2. Consider a photon that scatters from an electron at rest. If the photon scatters at an angle 60° with a wavelength (λ’) that is twice its incident wavelength (λ), then the angle at which the electron recoils will be _________ degrees. (Answer should be an integer.)**

Answer: 30

**Q3. For a particle in a one dimensional box, the ground state energy is given by E _{0}. The allowed energies of such a particle are**

a) 2E

_{0}

**b) 4E**

_{0}c) 6E

_{0}

**d) 9E**

_{0}**Answer: b) 4E _{0}, d) 9E_{0}**

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

**Q4. Consider a particle in a two dimensional box whose ground state energy is € _{0}. Then the energy E = 13€_{0} is two fold degenerate.**

a) True

b) False

**Answer: a) True**

**Q5. Suppose the 2nd energy level of a particle in a cubical box is given by E = 6E _{g} where E_{g}, is the ground state energy. Then the immediate 3rd energy level will be ______ fold degenerate. (Answer should be an integer.)**

Answer: 3

**Q6. The non-zero commutator brackets are****a) [z, p _{x}]**

b) [z,p

_{y}]

**c) [x^2, p**

_{x}]**d) [x, p**

_{x}^{2}]**Answer: a), c), d)**

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

Q7.

**Answer: c) √15/16a ^{5}**

Q8.

**Answer: d**

**Q9. The normalized wavefunction of a particle is Ψ(x) = Aexp(iax – ibt), where A, a and b are constants. The uncertainty in its momentum is**

a) ha

b) h^{2}a^{2}

c) 0

d) -ha

**Answer: c) 0**

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

Q10.

**Answer: b) False**

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

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