# Quantum Mechanics 1 | Week 2

**Session: JAN-APR 2024**

**Course name: Quantum Mechanics I**

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#### These are Quantum Mechanics 1 Week 2 Assignment Nptel Answers

#### Q1. A particle of mass m is confined to move in a potential of the form

V(x)={0, 0≤x≤a

∞, otherwise

The wavefunction of the particle at time t = 0 is given by

(x,0)=Asin(5πх/a)cos(2πx/a)

Normalized (x, 0) can be written as

a) 2/√a(sin(5πх/a)+sin(2πx/a))

b) 2/√a(sin(7πх/a)+sin(7πx/a))

c) 1/√a(sin(5πх/a)+sin(2πx/a))

d) 1/√a(sin(7πх/a)+sin(7πx/a))

**Answer: d) 1/√a(sin(7πх/a)+sin(7πx/a))**

**Q2.**

**Answer: a) True**

**Q3. A particle of mass m is trapped in the potentialV={0, -a≤x≤a{∞, otherwiseThe probability of finding the trapped particle between x = 0 and x = a/n, when it is in the nth state is 1/n.**

a) True

b) False

**Answer: a) True**

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**These are Quantum Mechanics 1 Week 2 Assignment Nptel Answers**

**Q4. An electron is confined in the ground state of a one-dimensional harmonic oscillator such that the uncertainty in position Δ(x) = 10^-10m. If the expectation values of kinetic and potential energy are same, i.e. (T) = (V), then the energy required to excite the electron to its first excited state is ______eV. (Write upto two decimal places.)(Hint : Use h =1.05 x 10^-34 Js, m = 9.1 x 10-³¹ kg)**

Answer: 3.97 (Type: Range) 3.00,4.00

**Q5.**

**Answer: b)**

**Q6.**

**Answer: a)**

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**These are Quantum Mechanics 1 Week 2 Assignment Nptel Answers**

**Q7. For a potential barrier of height Up and finite width b, the position space wavefunction (x) will be oscillatory for any x if and only if energy E of the particle is**

a) greater than Uo

b) zero

c) less than Uo

d) negative

**Answer: a) greater than Uo**

**Q8. A 1eV electron got trapped inside the surface of a metal. If the potential barrier is 4.0eV and the width of the barrier is 2Å, then the transmission co-efficient T is**

a) 1

b) 0.25

c) 0.85

d) 0.085**(Hint : Use h = 1.05 x 10^-34 Js, m= 9.1 x 10^-31 kg)**

**Answer: d) 0.085**

**These are Quantum Mechanics 1 Week 2 Assignment Nptel Answers**

**Q9. Consider a potential step of form,V(x) ={0, x < 0Vo, x ≥0A beam of particles with energy E approach this potential step from left. Then the statement that best describes the reflection coefficient (R) is**

a) R is non-zero when E > Vo, R = 1 when E < Vo

b) R = 0 when E > Vo, R = 1 when E < Vo.

c) R = 1 when E > Vo, R = 0 when E < Vo.

d) R is non-zero when E > Vo, R = 0 when E < Vo.

**Answer: a) R is non-zero when E > Vo, R = 1 when E < Vo**

**These are Quantum Mechanics 1 Week 2 Assignment Nptel Answers**

**Q10. For an infinite square well potential, if the width of the well decreases, what happens to the zeropoint energy (Eo) and momentum uncertainty (Δp)?**

a) both Eo and Δp decrease

b) both Eo and Δp increase

c) Eo decreases and Δp increases

d) Eo increases and Δp decreases

**Answer: b) both Eo and Δp increase**

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**These are Quantum Mechanics 1 Week 2 Assignment Nptel Answers**

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