Postulates Of Quantum Mechanics MCQ Level - 2


10 Questions MCQ Test Modern Physics for IIT JAM | Postulates Of Quantum Mechanics MCQ Level - 2


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This mock test of Postulates Of Quantum Mechanics MCQ Level - 2 for Physics helps you for every Physics entrance exam. This contains 10 Multiple Choice Questions for Physics Postulates Of Quantum Mechanics MCQ Level - 2 (mcq) to study with solutions a complete question bank. The solved questions answers in this Postulates Of Quantum Mechanics MCQ Level - 2 quiz give you a good mix of easy questions and tough questions. Physics students definitely take this Postulates Of Quantum Mechanics MCQ Level - 2 exercise for a better result in the exam. You can find other Postulates Of Quantum Mechanics MCQ Level - 2 extra questions, long questions & short questions for Physics on EduRev as well by searching above.
QUESTION: 1

Consider a set of wave functions ψi(x). Which of the following condition guarantees that the functions are normalized and mutually orthogonal? (i, j  take values from 1 to n)

Solution:

For the states to be orthogonal

and for them to be normalised,


QUESTION: 2

The phase velocity of ripples on a liquid surface is   where S is the surface tension and ρ the density of the liquid. The group velocity of the ripples is given by :

Solution:


As wave number,

We know that group velocity given by

The correct answer is: 

QUESTION: 3

The solutions of a free particle are :

Solution:


V = 0 for a free particle
 ∴  

Schrödinger equation.

  (General solution)
∴    Aeikx   and  Be–ikx  are solution to the free particle

The correct answer is: Energy and momentum eigen functions with both positive and negative momentum eigenvalues.

QUESTION: 4

The wave function for a particle constrained to move in 1D is shown in the graph below.

What is the probability that the particle would be found between x = 2 and x = 4 ?

Solution:



The correct answer is:  13/16

QUESTION: 5

The probability current density  is given as   Which of the following is true?

Solution:

From the continuity equation


 

i.e. p is constant in time

 Probability current density
The correct answer is: If     then probability density is constant in time.

QUESTION: 6

Smallest possible uncertainty in position of the electron moving with velocity 3 × 107 m/s. Given, h = 6.63 × 10–34 Js, m0 = 9.1 × 10–31 kg.

Solution:

Given, v = 3 × 107 m/s
Let    Δxmin be the minimum uncertainty in position of the electron and Δp the maximum uncertainty in the momentum of the electron.

Thus, we have,

= 0.03867 × 0.9949 × 10–10 m
= 3.8 × 10–12 m
The correct answer is: 3.8 × 10–12 m

QUESTION: 7

Choose the correct statement

Solution:

The correct answer is: All the energy eigenvalues are always real.

QUESTION: 8

Choose the correct statement

Solution:

1. 
2.   from the definition of uncertainty
3.   Uncertainty principle
The correct answer is: All of the above

QUESTION: 9

A linear harmonic oscillator of mass m oscillates with a frequency  where k is its force constant. What is the minimum energy of the oscillator.

Solution:

The energy of the linear harmonic oscillator is

This is a constant of motion. We can represent the constant value of E by means of averages of the kinetic and potential over a cycle of motion by writing.

The average value of x and p should vanish for an oscillating particle. So, we can identifywith the square of the corresponding uncertainties.

Since from the uncertainty principle  To determine the minimum energy of the oscillator, we put

The minimum energy is

QUESTION: 10

Choose the correct statement for a free particle with  ψ(x) = Aeikx

Solution:

V = 0 for a free particle
 ∴  
Schrödinger equation.


 

∴  Aeikx and Be–ikx     (General solution)
∴  are solution to the free particle

The correct answer is: Energy eigenvalue is   and momentum is  

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