This set of Engineering Physics Multiple Choice Questions & Answers (MCQs) focuses on “Schrodinger Equation (Time Dependent Form)”.

1. Which of the following is the correct expression for the Schrödinger wave function?

a) \(i\hbar \frac{d\Psi}{dt} = -i\frac{\hbar}{2m} \frac{\partial\Psi}{\partial x}+ U\Psi\)

b) \(i\hbar \frac{d\Psi}{dt} = -i\frac{\hbar}{2m} \frac{\partial^2 \Psi}{\partial x^2}+ U\Psi\)

c) \(i\hbar \frac{d\Psi}{dt} = -i\frac{\hbar^z}{2m} \frac{\partial\Psi}{partial x}+ U\Psi\)

d) \(i\hbar \frac{d\Psi}{dt} = -i\frac{\hbar^z}{2m} \frac{\partial^2\Psi}{\partial x^2}+ U\Psi \)

View Answer

Explanation: The correct expression for the Schrödinger wave equation is \(i\hbar \frac{d\Psi}{dt}= -i\frac{\hbar^z}{2m} \frac{\partial^2\Psi}{\partial x^2}+ U\Psi \). Schrodinger equation is a basic principle in itself.

2. For a quantum wave particle, E = _____________

a) ℏ k

b) ℏ ω

c) ℏ ω/2

d) ℏ k/2

View Answer

Explanation: 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.

3. Schrodinger Wave equation can be derived from Principles of Quantum Mechanics.

a) True

b) False

View Answer

Explanation: Schrodinger equation is a basic principle in itself. It cannot be derived from other principles of physics. Only, it can be verified with other principles.

4. Which of the following can be a wave function?

a) tan x

b) sin x

c) cot x

d) sec x

View Answer

Explanation: 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.

5. Which of the following is not a characteristic of wave function?

a) Continuous

b) Single valued

c) Differentiable

d) Physically Significant

View Answer

Explanation: The wave function has no physical significance. It merely helps in determining the state of a particle. It is the square of the wave function that has a physical significance.

6. Find the function, f(x), for which X f(x) = \(-\frac{i}{\hbar}a^2p_xf(x),\) where a is the real quantity.

a) ke^{-x2}

b) ke^{-x2/2a}

c) ke^{-x2/2a2}

d) ke^{-x2/2a}

View Answer

Explanation: Now, given that, X f(x) = \(-\frac{i}{\hbar}a^2p_xf(x).\)

X f(x) = \(-\frac{i}{\hbar}a^2p_xf(x)/dx\)

df/f = -xdx/a

^{2}

ln f = -x

^{2}/2a

^{2}+ C

f = ke

^{-x2/2a2}.

7. dΨ/dx must be zero.

a) True

b) False

View Answer

Explanation: For a wave function, dΨ/dx, must be continuous and single-valued everywhere, just like Ψ. Also, Ψ must be normalizable.

8. Any wave function can be written as a linear combination of _________________

a) Eigen Vectors

b) Eigen Values

c) Eigen Functions

d) Operators

View Answer

Explanation: A wave function describes the state of a particle. It does not have a physical significance. Moreover, it can be written as a linear combination of Eigen functions, i.e., Ψ(x) = AF(x) + BG(x).

9. The Schrödinger is a differential equation.

a) True

b) False

View Answer

Explanation: The Schrodinger wave equation generated is a partial differential equation. It is a basic principle in itself and cannot be derived from other principles of physics. There are two types of partial differential equation time dependent form and steady-state form.

10. Which of the following can be a solution of Schrodinger equation?

a)

b)

c)

d)

View Answer

Explanation: Out of the following, only the below diagram can be the solution of the Schrodinger Wave equation. because other diagram does not have a continuous dΨ/dx. Some diagrams are double valued and discontinuous also.

**Sanfoundry Global Education & Learning Series – Engineering Physics.**

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