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QUESTION: 1

Probability of finding a particle between 0 to 0.5** L** in a one-dimensional box of length

Solution:

The correct answer is: 1/2

QUESTION: 2

For the case of even parity solution of a symmetric infinite potential well, what is true for expectation value of x, p, x^{2} and p^{2} ?

Solution:

**Correct Answer :- d**

**Explanation :** φ = A cos nπx/L

x = φxφ dx

= A^{2} ∫(0 to L) xcos^{2} nπx/L dx

= A^{2} ∫(0 to L) x/2(cos^{2 }nπx/L - 1) dx

= (A^{2})/2 ∫(0 to L) xcos^{2} nπx/L dx

= 0

p = d/dt (x)

= 0

QUESTION: 3

Which of the following can be a wave function?

Solution:

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.

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?

Solution:

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

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.

Solution:

For particle in a box

For ψ_{1}(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...)

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

Solution:

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

QUESTION: 7

For a quantum wave particle, E = _____________

Solution:

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.

QUESTION: 8

Consider the potential of the form

V(x) = 0 for x __ <__ a

= V

= 0 for x

Which of the following wave functions is possible for a particle incident from the left with energy E < V_{0}

Solution:

Solving the Schrodinger equation for the region from ** a** to

So, in the region from **x****= a** to

QUESTION: 9

An electron is trapped in an infinite well of width 1** cm**. For what value of

Solution:

The correct answer is: ~ 10^{7}

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

Solution:

The correct answer is: 6 **MeV**

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