Virtual Labs

1. For an electron in a 1D infinite potential well of width L, which energy levels are allowed?

a: E = 0 only Explanation

Explanation

b: Any continuous value of E Explanation

Explanation

c: E = n²π²ħ² / (2mL²), where n is an integer Explanation

Explanation

d: E = mgh Explanation

Explanation

2. Which of the following affects the number of bound states in a finite potential well?

a: The shape of the wavefunction Explanation

Explanation

b: The depth and width of the potential well Explanation

Explanation

c: The mass of the observer Explanation

Explanation

d: The time of observation Explanation

Explanation

3. The wavefunction of a particle in an infinite well of width L is zero at:

a: x = 0 and x = L only Explanation

Explanation

b: At multiple discrete points inside the well Explanation

Explanation

c: Everywhere inside the well Explanation

Explanation

d: No point at all Explanation

Explanation

4. What does the square of the wave function ψ(x) represent in quantum mechanics?

a: Electric field strength Explanation

Explanation

b: Probability density of finding the particle at x Explanation

Explanation

c: Potential energy at position x Explanation

Explanation

d: Total energy of the system Explanation

Explanation

5. In a finite potential well, what happens to the wavefunction outside the well?

a: It abruptly becomes zero Explanation

Explanation

b: It grows exponentially Explanation

Explanation

c: It decays exponentially Explanation

Explanation

d: It oscillates indefinitely Explanation

Explanation

6. Why are only discrete energy levels allowed in an infinite potential well?

a: Because of wave interference at the walls Explanation

Explanation

b: Because electrons prefer certain energies Explanation

Explanation

c: Due to thermal equilibrium Explanation

Explanation

d: Because quantum mechanics breaks down at the nanoscale Explanation

Explanation

7. The momentum of a particle in an infinite potential well is most closely related to:

a: The width of the well and quantum number n Explanation

Explanation

b: The potential barrier height Explanation

Explanation

c: The mass of the observer Explanation

Explanation

d: The charge of the particle Explanation

Explanation

8. How does increasing the width of an infinite potential well affect the energy levels?

a: Energy levels remain the same Explanation

Explanation

b: Energy levels become more closely spaced Explanation

Explanation

c: Energy levels become more widely spaced Explanation

Explanation

d: It has no effect on the energy levels Explanation

Explanation

9. Why does quantum tunneling occur in a finite potential well?

a: Because classical mechanics allows it Explanation

Explanation

b: Because the particle can gain energy temporarily Explanation

Explanation

c: Because the wavefunction is nonzero in classically forbidden regions Explanation

Explanation

d: Because particles travel faster than light Explanation

Explanation

Schrodinger Wave Equation and Solution