A particle is incident with a constant energy E on a one-dimensional potential barrier as shown in the figure.<br><img src="/images/question-image/engineering-physics/quantum-mechanics/1689583731-a-particle-is-incident-with-a-constant.png" title="Quantum Mechanics mcq question image" alt="Quantum Mechanics mcq question image"><br>The wave functions in regions I and II are respectively

A particle of mass m is confined in the potential
Quantum Mechanics mcq question image

\[V\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{1}{2}m{\omega ^2}{x^2},}&{{\text{for }}x Let the wave function of the particle be given by $$\psi \left( x \right) = - \frac{1}{{\sqrt 5 }}{\psi _0} + \frac{2}{{\sqrt 5 }}{\psi _1}$$
where $${\psi _0}$$ and $${\psi _1}$$ are the eigen functions of the ground state and the first excited slate respectively. The expectation value of the energy is

A

$$\frac{{31}}{{10}}\hbar \omega $$

B

$$\frac{{25}}{{10}}\hbar \omega $$

C

$$\frac{{13}}{{10}}\hbar \omega $$

D

$$\frac{{11}}{{10}}\hbar \omega $$

A particle with energy E is in a time independent double well potential as shown in the figure. Which, of the following statements about the particle is not correct?
Quantum Mechanics mcq question image

A

The particle will always be in a bound state

B

The probability of finding the particle in one well will be time dependent

C

The particle will be confined to anyone of the wells

D

The particle can tunnel from one well to the other and back

A particle of mass m is confined in an infinite potential well \[V\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {0,}&{{\text{if }}0 It is subjected to a perturbing potential $${V_P}\left( x \right) = {V_0}\sin \left( {\frac{{2\pi x}}{L}} \right)$$ within the well. Let E⁽¹⁾ and E⁽²⁾ be the corrections to the ground state energy in the first and second order in V₀.
Quantum Mechanics mcq question image

Which of the following is correct?

A

[

A. E⁽¹⁾ = 0; E⁽²⁾

B. E⁽¹⁾ > 0; E⁽²⁾ = 0

B

E⁽¹⁾ = 0; E⁽²⁾ depends on the sign of V₀

C

E⁽¹⁾ (2)

There are only three bound states for a particle of mass m in a one-dimensional potential well of the form shown in the figure. The depth V₀ of the potential satisfies
Quantum Mechanics mcq question image

A

[

A. $$\frac{{2{\pi ^2}{\hbar ^2}}}{{m{a^2}}}

B. $$\frac{{{\pi ^2}{\hbar ^2}}}{{m{a^2}}}

B

$$\frac{{2{\pi ^2}{\hbar ^2}}}{{m{a^2}}}

C

$$\frac{{2{\pi ^2}{\hbar ^2}}}{{m{a^2}}}

A particle of mass m is attached to a thin uniform rod of length a and mass 4m. The distance of the particle from the centre of mass of the rod is $$\frac{a}{2}.$$
Classical Mechanics mcq question image

The moment of inertia of the combination about an axis passing through a normal to the rod is

A

$$\frac{{64}}{{48}}m{a^2}$$

B

$$\frac{{91}}{{48}}m{a^2}$$

C

$$\frac{{27}}{{48}}m{a^2}$$

D

$$\frac{{51}}{{48}}m{a^2}$$

A vertically immersed surface is shown in the below figure. The distance of its centre of pressure from the water surface is
Hydraulics and Fluid Mechanics in ME mcq question image

Hydraulics and Fluid Mechanics in ME mcq question image

A

$$\frac{{{\text{b}}{{\text{d}}^2}}}{{12}} + \overline {\text{x}} $$

B

$$\frac{{{{\text{d}}^2}}}{{12\overline {\text{x}} }} + \overline {\text{x}} $$

C

$$\frac{{{{\text{b}}^2}}}{{12}} + \overline {\text{x}} $$

D

$$\frac{{{{\text{d}}^2}}}{{12}} + \overline {\text{x}} $$

Two blocks ‘A’ and ‘B’ of masses 150 kg and 50 kg respectively are connected by means of a string as shown in the below figure. The tension in all the three strings __________ be same.
Engineering Mechanics mcq question image

Engineering Mechanics mcq question image

A

Will

B

Will not

C

Either A or B

D

None of these

In a framed structure, as shown in the below figure, the forces in the members AB and BC are respectively
Engineering Mechanics mcq question image

A

$$\sqrt 3 \,\,$$W (tensile) and 2W (compressive)

B

2W (tensile) and $$\sqrt 3 \,\,$$W (compressive)

C

$$2\sqrt 3 \,\,$$W (tensile) and $$2\sqrt 3 \,\,$$W (compressive)

D

None of the above

A weight of 100 kg is supported by a string whose ends are attached to pegs ‘A’ and ‘B’ at the same level shown in below figure. The tension in the string is
Applied Mechanics and Graphic Statics mcq question image

Applied Mechanics and Graphic Statics mcq question image

A

50 kg

B

750 kg

C

100 kg

D

120 kg

The beam shown in below figure is supported by a hinge at ‘A’ and a roller at ‘B’. The reaction RA of the hinged support ‘A’ of the beam, is
Applied Mechanics and Graphic Statics mcq question image

A

10.8 t

B

10.6 t

C

10.4 t

D

10.2 t

A particle is incident with a constant energy E on a one-dimensional potential barrier as shown in the figure.

The wave functions in regions I and II are respectively

Related Questions

A particle is incident with a constant energy E on a one-dimensional potential barrier as shown in the figure.The wave functions in regions I and II are respectively

Related Questions

A particle is incident with a constant energy E on a one-dimensional potential barrier as shown in the figure.

The wave functions in regions I and II are respectively