Virtual Labs

Schordinger Wave Equation and Infinite and Finite potential well

1. What is the wave function (ψ) in quantum mechanics?

a: A function that describes the shape of an electron's location. Explanation

Explanation

b: A function that gives the probability of finding the particle. Explanation

Explanation

c: A function that describes the energy levels of an atom. Explanation

Explanation

d: A function that gives the velocity of a particle. Explanation

Explanation

2. What are the allowed energy levels in the solution for a particle in a one-dimensional infinite potential well of width

L

? What are the allowed energy levels?

E_n = \frac{n^2 h^2}{2mL^2}

Explanation

E_n = \frac{n^2 \pi^2 \hbar^2}{2mL^2}

Explanation

E_n = \frac{n \hbar}{2mL}

Explanation

E_n = \frac{n^2 h}{mL^2}

Explanation

3. Which of the following describes a finite potential well?

a: A potential well with infinitely high walls. Explanation

Explanation

b: A potential well with finite energy outside the well. Explanation

Explanation

c: A potential that is zero everywhere. Explanation

Explanation

d: A potential well with finite depth and width. Explanation

Explanation

4. Calculate the probability of finding a particle in a specific region within an infinite potential well if the wave function is given by

\psi(x) = \sqrt{\frac{2}{L}} \sin\left(\frac{n\pi x}{L}\right)

. Assume

n = 1

and

L = 1

1

Explanation

0.5

Explanation

0.75

Explanation

0.25

Explanation

5. In a system which is invert of 1D finite potential well (i.e. system potential barrier V(x) exists, between x=0 and x=L and particle is free in d: 0.25 all other regions (x<0 and x>L). If particle is located in x<0 and moving towards x=0, what will be characteristics of SWE solution (wavefunction) is the barrier and in the free space?

a: Particle has a sinusoidal wave function every where Explanation

Explanation

b: Particle has a decaying wave function everywhere Explanation

Explanation

c: Particle cannot exist in this system Explanation

Explanation

d: Particle wavefunction is sinusoidal in x<=0 and x>=L and decays exponentially 0 Explanation

Explanation

6. For above system, which of the following will be true?

a: Particle wave function should be zero for x>= L Explanation

Explanation

b: Particle wave function amplitude will increase for x>=L Explanation

Explanation

c: Particle will bounce back completely at x=0 Explanation

Explanation

d: Larger the value of L, lower is the amplitude of wavfunction for x>=L Explanation

Explanation