Application Of Schrodinger Wave Equation – MSQ

# Application Of Schrodinger Wave Equation – MSQ

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Application Of Schrodinger Wave Equation – MSQ for Physics 2023 is part of Topic wise Tests for IIT JAM Physics preparation. The Application Of Schrodinger Wave Equation – MSQ questions and answers have been prepared according to the Physics exam syllabus.The Application Of Schrodinger Wave Equation – MSQ MCQs are made for Physics 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Application Of Schrodinger Wave Equation – MSQ below.
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Application Of Schrodinger Wave Equation – MSQ - Question 1

### Consider two cases of one dimensional potential well. The first case is an infinite potential will  V = 0,  for  a < x < 0  the second case is a finite potential well. Which of the following is true? [for  E < V0]

Detailed Solution for Application Of Schrodinger Wave Equation – MSQ - Question 1

The correct answers are:  for infinite case &  for finite case  for infinite case &   for the finite case

*Multiple options can be correct
Application Of Schrodinger Wave Equation – MSQ - Question 2

### The Steady-state form of Schrodinger wave equation is _____________

Detailed Solution for Application Of Schrodinger Wave Equation – MSQ - Question 2

The Steady-state Schrodinger Wave equation is a linear in the wave function Ψ. It means, that no term has \Psi with a degree greater than 1.

*Multiple options can be correct
Application Of Schrodinger Wave Equation – MSQ - Question 3

### For a wave function ψ(x) , its time dependence can be seen from  Select the correct option.

Detailed Solution for Application Of Schrodinger Wave Equation – MSQ - Question 3

is normalised, so is  & neither of has any time dependence.

The correct answers are: If  is normalised, then  has to be normalised, Neither of  has any time dependence

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Application Of Schrodinger Wave Equation – MSQ - Question 4

Consider the solutions to particle in one dimensional box of length, L.

Which of the following is true for the group of functions  ψ2(x)

Detailed Solution for Application Of Schrodinger Wave Equation – MSQ - Question 4

The solution of a symmetric infinite potential well consists of

Now, any function can be written as a linear combination of these functions (sin and cos)

They form a complete let

The correct answers are: They are alternately even and odd with respect to the centre of the well, As we go up in energy, each successive state has one more node. i.e.  ψ1(x) has none, ψ2(x) has one, ψ3(x) has 2 and so on, They are mutually orthogonal, They form a complete set

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Application Of Schrodinger Wave Equation – MSQ - Question 5

Choose the correct option.
For the case of particle in a one dimensional box.

Detailed Solution for Application Of Schrodinger Wave Equation – MSQ - Question 5

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Application Of Schrodinger Wave Equation – MSQ - Question 6

For the above cases of one-dimensional infinite and finite potential wells which of the following is true?

Detailed Solution for Application Of Schrodinger Wave Equation – MSQ - Question 6

Energy levels are same!

The correct answer is: Energy levels are same,  in both cases.

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Application Of Schrodinger Wave Equation – MSQ - Question 7

For a particle in a one dimensional box,

There is zero probability of finding the particle at

Detailed Solution for Application Of Schrodinger Wave Equation – MSQ - Question 7

Probability is 0 at x = 0 & a
For

Probability density is zero at x = 0, a/2 , a

Probability density zero at x = 0,

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Application Of Schrodinger Wave Equation – MSQ - Question 8

Which of the following is true in case of a free particle?

Detailed Solution for Application Of Schrodinger Wave Equation – MSQ - Question 8

The Schrodinger equation solution are

∴  momentum eigenfunction.

The correct answers are: The Schrodinger equation yields the solution to be  (linear combination of the two), The solutions of the Schrodinger equation are both energy and momentum eigenfunctions

*Multiple options can be correct
Application Of Schrodinger Wave Equation – MSQ - Question 9

In any arbitrary potential, an acceptable solution of the Schrodinger equations must satisfy which of the following properties?

Detailed Solution for Application Of Schrodinger Wave Equation – MSQ - Question 9

The correct answers are: The gradient of the solution must be single valued, finite and continuous at the every point, The gradient should also be bounded at large distances, The wave function must be continuous throughout, The wave function must vanish at the point where the potential approaches infinity

*Multiple options can be correct
Application Of Schrodinger Wave Equation – MSQ - Question 10

Which of the following is true for a quantum harmonic oscillator?

Detailed Solution for Application Of Schrodinger Wave Equation – MSQ - Question 10

for a harmonic oscillator

∴   evenly spaced.

The correct answers are: A spectrum of evenly spaced energy levels, A non zero probability of finding the oscillator outside the classical turning points

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