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Quantum Mechanics of a particle in a potential well

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1. What does the quantum number n represent in the Schrödinger equation?

a: The amplitude of the wavefunction Explanation

Explanation

b: The energy level of the particle Explanation

Explanation

c: The length of the box Explanation

Explanation

d: The time interval Explanation

Explanation

2. What is the purpose of the time-dependent part of the wavefunction in the equation?

a: To describe the spatial distribution of the particle Explanation

Explanation

b: To describe the amplitude of the wavefunction Explanation

Explanation

c: To describe how the wavefunction evolves over time Explanation

Explanation

d: To calculate the value of n Explanation

Explanation

3. What happens to the energy levels when the width of a potential well decreases?

a: Energy levels move closer together Explanation

Explanation

b: Energy levels remain unchanged Explanation

Explanation

c: Energy levels become more widely spaced Explanation

Explanation

d: Energy levels become continuous Explanation

Explanation

4. Which statement correctly describes the wavefunction inside an infinite potential well?

a: The wavefunction is zero everywhere Explanation

Explanation

b: The wavefunction is sinusoidal inside the well and zero at the boundaries Explanation

Explanation

c: The wavefunction is constant throughout the well Explanation

Explanation

d: The wavefunction increases linearly with position Explanation

Explanation

5. Why can't a particle in an infinite potential well have zero energy (E = 0)?

a: Because zero energy violates the uncertainty principle Explanation

Explanation

b: Because the particle has too much mass Explanation

Explanation

c: Because the well width is infinite Explanation

Explanation

d: Because the time-dependent wavefunction becomes undefined Explanation

Explanation

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