Application Of Schrodinger Equation MCQ

# Application Of Schrodinger Equation MCQ

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Application Of Schrodinger Equation MCQ - Question 1

### Probability of finding a particle between 0 to 0.5L in a one-dimensional box of length L in the second excited state is :

Detailed Solution for Application Of Schrodinger Equation MCQ - Question 1   Application Of Schrodinger Equation MCQ - Question 2

### For the case of even parity solution of a symmetric infinite potential well, what is true for expectation value of x, p, x2 and p2 ?

Detailed Solution for Application Of Schrodinger Equation MCQ - Question 2

Explanation : φ = A cos nπx/L

x = φxφ dx

= A2 ∫(0 to L) xcos2 nπx/L dx

= A2 ∫(0 to L) x/2(cosnπx/L - 1) dx

= (A2)/2 ∫(0 to L) xcos2 nπx/L dx

= 0

p = d/dt (x)

= 0

Application Of Schrodinger Equation MCQ - Question 3

### Which of the following can be a wave function?

Detailed Solution for Application Of Schrodinger Equation MCQ - Question 3

Out of all the given options, sin x is the only function, that is continuous and single-valued. All the rest of the functions are either discontinuous or double-valued.

Application Of Schrodinger Equation MCQ - Question 4

Consider the case of an infinite square well potential symmetric about the y axis i.e. Which of the following is a true?

Detailed Solution for Application Of Schrodinger Equation MCQ - Question 4 The correct answer is: Infinite square well which is not symmetric about the y axis, has only odd parity states, whereas the asymmetric potential well has both even & odd parity states

Application Of Schrodinger Equation MCQ - Question 5

The solution to the Schrodinger equation for a particle bound in a one-dimensional, infinitely deep potential well, indexed by a quantum number n, indicates that in the middle of the well, the probability density vanishes for.

Detailed Solution for Application Of Schrodinger Equation MCQ - Question 5

For particle in a box For ψ1(x), probability density does not vanish in the middle
for probability density vanishes in the middle

Similarly, it does not vanish for vanishes for in the middle of the well.

The correct answer is: states of even n(n = 2, 4...)

Application Of Schrodinger Equation MCQ - Question 6

For a particle of mass m, being acted upon by a force with potential energy function a one-dimensional simple harmonic oscillator. If there is a wall at x = 0 so that  V = ∞ for x < 0, then the energy levels are equal to :

Detailed Solution for Application Of Schrodinger Equation MCQ - Question 6

The probability distributions for the quantum states of the oscillator without the barrier. Infinite barrier at the origin means a node at origin, or the wave function goes to zero at x = 0.

By symmetry, the ground state will disappear, as well all the even states.  Odd values remain Application Of Schrodinger Equation MCQ - Question 7

For a quantum wave particle, E = _____________

Detailed Solution for Application Of Schrodinger Equation MCQ - Question 7

The Energy of a wave particle is given as ℏ ω while the momentum of the particle is given as ℏ k. These are the desired relation.

Application Of Schrodinger Equation MCQ - Question 8

Consider the potential of the form V(x) = 0 for x < a
= V0 for a < x b
= 0 for x > b

Which of the following wave functions is possible for a particle incident from the left with energy E < V0

Detailed Solution for Application Of Schrodinger Equation MCQ - Question 8

Solving the Schrodinger equation for the region from a to b.  So, in the region from x a to b, the wave function are in the form of exponential rise/fall. Application Of Schrodinger Equation MCQ - Question 9

An electron is trapped in an infinite well of width 1cm. For what value of n will the electron have an energy of 2eV?

Detailed Solution for Application Of Schrodinger Equation MCQ - Question 9 The correct answer is: ~ 107

Application Of Schrodinger Equation MCQ - Question 10

If the nucleus is seen as a cubical box of length 10–14 m, then compute the minimum energy of a nucleon confined to the nucleus. Mass of nucleon = 1.6 × 10–27 kg

Detailed Solution for Application Of Schrodinger Equation MCQ - Question 10  The correct answer is: 6 MeV

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