Virtual Labs

Schordinger Wave Equation and Infinite and Finite potential well

1. Explain the difference between an infinite potential well and a finite potential well.

a: An infinite potential well has infinite energy levels, while a finite potential well has finite energy levels. Explanation

Explanation

b: An infinite potential well has infinitely high walls, while a finite potential well has walls with finite height. Explanation

Explanation

c: An infinite potential well has a continuous spectrum of energy, while a finite potential well has a discrete spectrum. Explanation

Explanation

d: An infinite potential well has zero probability of finding a particle outside the well, while a finite potential well has non-zero probability. Explanation

Explanation

2. For an electron in an infinite potential well of width

L

, calculate the energy of the second excited state (

n=3

E = \frac{9\pi^2\hbar^2}{2mL^2}

Explanation

E = \frac{6\pi^2\hbar^2}{mL^2}

Explanation

E = \frac{3\pi\hbar}{mL}

Explanation

E = \frac{9\pi\hbar^2}{2mL}

Explanation

3. What does the square of the wave function (|ψ|^2) represent in the context of quantum mechanics?

a: The velocity of the particle. Explanation

Explanation

b: The energy of the particle. Explanation

Explanation

c: The probability density of finding the particle at a given position. Explanation

Explanation

d: The force acting on the particle. Explanation

Explanation

4. Given the wave function

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

for a particle in an infinite potential well, what is the probability of finding the particle in the first quarter of the well (0 to

L/4

) for the ground state (

n=1

a: 0.25 Explanation

Explanation

b: 0.5 Explanation

Explanation

c: 0.125 Explanation

Explanation

d: 0.75 Explanation

Explanation

5. Which of these cannot be best explained using SWE ?

a: Electron cloud around atoms. Explanation

Explanation

b: Hole moving in silicon lattice Explanation

Explanation

c: Quantum dot Explanation

Explanation

d: motion of planets around star Explanation

Explanation