Virtual Labs

Quantum Mechanics of a Linear Harmonic Oscillator

1. After using the simulation, what did you observe when you set the coherent state with α = 3?

a: The wavefunction remained stationary Explanation

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b: The probability density oscillated back and forth like a classical particle Explanation

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c: The wavefunction disappeared Explanation

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d: Only the ground state was visible Explanation

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2. In the simulation, when you switched between Real/Imaginary and Density/Phase views, what did the color represent in Density/Phase mode?

a: The energy of the state Explanation

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b: The amplitude of the wavefunction Explanation

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c: The local phase of the wavefunction Explanation

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d: The probability density Explanation

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3. When you set the 'First Excited (n=1)' preset, what was the Expected Energy shown in the Live Data panel?

a: 0.500 ℏω Explanation

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b: 1.000 ℏω Explanation

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c: 1.500 ℏω Explanation

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d: 2.000 ℏω Explanation

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4. In the phasor clock representation, what did the length of the clock hand represent?

a: The phase of that eigenstate Explanation

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b: The energy of that eigenstate Explanation

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c: The amplitude (coefficient magnitude) of that eigenstate Explanation

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d: The frequency of that eigenstate Explanation

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5. What happened to the Total Probability value when you clicked the 'Normalize' button?

a: It became 0 Explanation

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b: It became 1.000 Explanation

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c: It became undefined Explanation

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d: It doubled Explanation

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6. When you observed the superposition of n=0 and n=1 states, why did the probability density oscillate?

a: Because of numerical errors in the simulation Explanation

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b: Because the two states have different energies and thus different time evolution phases Explanation

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c: Because the amplitude changes randomly Explanation

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d: Because the simulation is in Real/Imaginary mode Explanation

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7. What did you observe about the speed of phasor clock rotation for higher energy states (larger n)?

a: All clocks rotated at the same speed Explanation

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b: Higher n states rotated slower Explanation

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c: Higher n states rotated faster Explanation

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d: Only even n states rotated Explanation

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8. Based on your observations, which statement correctly describes the difference between classical and quantum harmonic oscillators?

a: Both have continuous energy levels Explanation

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b: Classical can have zero energy, quantum cannot (has zero-point energy) Explanation

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c: Both have the same ground state energy Explanation

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d: Quantum has no wavefunction Explanation

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9. When you created a 'Random' state and looked at the live data table, what relationship did you notice between amplitude and probability?

a: Probability = amplitude Explanation

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b: Probability = amplitude squared (|cₙ|²) Explanation

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c: Probability = square root of amplitude Explanation

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d: They are unrelated Explanation

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10. What did you learn about quantum superposition from this simulation?

a: A quantum system can only be in one state at a time Explanation

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b: A quantum system can exist as a combination of multiple states simultaneously Explanation

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c: Superposition violates conservation of energy Explanation

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d: Superposition is not visible in the wavefunction Explanation

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