Virtual Labs

Quantum Mechanics of a Particle in a Potential Well

1. In the simulation, when you increased the quantum number n from 1 to 5, what did you observe about the number of peaks (antinodes)?

a: Number of peaks decreased Explanation

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b: Number of peaks remained the same Explanation

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c: Number of peaks increased to match n Explanation

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d: Number of peaks became random Explanation

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2. When you enabled the |Ψ|² (probability) display, at which positions was the probability zero?

a: At the center of the box only Explanation

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b: At the boundaries and at the node positions Explanation

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c: Everywhere inside the box Explanation

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d: Probability was never zero Explanation

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3. Based on your observations, how did the energy change when you doubled the quantum number from n=2 to n=4?

a: Energy doubled Explanation

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b: Energy became 4 times larger Explanation

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c: Energy remained the same Explanation

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d: Energy decreased Explanation

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4. What did you observe about the wavelength when you increased the box length L?

a: Wavelength decreased Explanation

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b: Wavelength increased proportionally Explanation

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c: Wavelength remained constant Explanation

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d: Wavelength became zero Explanation

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5. In the Live Measurements panel, what was the relationship you observed between nodes and quantum number n?

a: Nodes = n Explanation

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b: Nodes = n + 1 Explanation

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c: Nodes = n - 1 Explanation

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d: Nodes = 2n Explanation

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6. When comparing the ground state (n=1) with excited states (n>1), what did you notice about where the particle is most likely to be found?

a: Always at the center for all states Explanation

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b: Always at the boundaries for all states Explanation

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c: At different positions depending on the quantum number Explanation

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d: Uniformly distributed for all states Explanation

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7. What happened to the oscillation frequency when you increased the quantum number n?

a: Oscillation became slower Explanation

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b: Oscillation became faster Explanation

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c: Oscillation speed remained unchanged Explanation

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d: Oscillation stopped completely Explanation

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8. From your graph of Energy vs Quantum Number, what type of relationship did you observe?

a: Linear relationship (straight line) Explanation

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b: Quadratic relationship (parabola) Explanation

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c: Inverse relationship (hyperbola) Explanation

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d: No clear relationship Explanation

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9. When you decreased the box length L while keeping n=3 constant, what happened to the energy value displayed?

a: Energy decreased proportionally Explanation

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b: Energy increased significantly Explanation

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c: Energy remained constant Explanation

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d: Energy became negative Explanation

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10. What did you observe about the wavefunction amplitude when you adjusted the Wave Amplitude slider?

a: It changed the energy levels Explanation

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b: It changed the quantum number Explanation

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c: It only changed the visual height of the wave without affecting physics Explanation

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d: It changed the wavelength Explanation

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