Step 1: Understanding the Interface

When you open the simulation, you will see three main panels:

Panel	Location	Contents
Control Panel	Left	Quantum parameters, preset states, quick actions, state amplitude sliders
Visualization	Center	Main canvas showing wavefunction, phasor clocks at bottom
Data & Info	Right	Live quantum data table, instructions, key concepts

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Step 2: Explore Preset Quantum States

Click on the preset buttons to observe different quantum behaviors:

Preset	Description	What to Observe
Ground State (n=0)	Lowest energy state	No nodes, Gaussian-shaped probability
First Excited (n=1)	First excited state	One node at center
Superposition	Equal mix of n=0 and n=1	Oscillating probability density
Coherent State	Classical-like oscillation	Wave packet moves back and forth
Equal Mix	All states equally weighted	Complex interference pattern
High Energy	Maximum quantum number	Many nodes visible

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Step 3: Control Animation Speed

1. Locate the Speed slider in the Quantum Parameters section
2. Move the slider to adjust the time evolution rate
3. Set to 0 to freeze the animation
4. Observe how different energy states rotate at different frequencies

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Step 4: Adjust Coherent State Parameter (α)

1. Use the Coherent State (α) slider to change the α value
2. Click the Coherent State preset button to apply
3. Larger α values create more classical-like behavior
4. Observe:
   • α = 0: Ground state only
   • α = 1-2: Small oscillation
   • α = 3-4: Large classical-like oscillation

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Step 5: Interact with Phasor Clocks

The phasor clocks at the bottom of the canvas represent each eigenstate:

1. Click and drag inside any clock circle
2. Distance from center sets the amplitude |c_n|
3. Angle sets the initial phase of that state
4. Release to see the wavefunction update immediately

Note: As you drag, real-time feedback shows:

• Current state number (n)
• Magnitude value
• Phase in degrees

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Step 6: Use Individual Amplitude Sliders

1. Scroll down in the left panel to find State Amplitudes
2. Each slider controls one eigenstate's amplitude (n=0 to n=7)
3. Adjust multiple sliders to create custom superpositions
4. Click Normalize to ensure total probability equals 1

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Step 7: Switch Visualization Modes

Toggle between two visualization modes:

Mode	Button	What It Shows
Real/Imaginary	📈 Real/Imaginary	Orange line: Real part of ψ; Cyan line: Imaginary part
Density/Phase	🌈 Density/Phase	Height shows probability density |ψ|²; Color shows local phase

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Step 8: Analyze Live Data

Observe the Live Quantum Data panel on the right:

1. Table shows:

   • State number (n)
   • Amplitude value
   • Probability |c_n|²

2. Total Probability: Should equal 1.000 when normalized

3. Expected Energy ⟨E⟩: Shows average energy in units of ℏω

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Step 9: Perform Experiments

Experiment A: Verify Energy Quantization

1. Set Ground State preset
2. Note the Expected Energy (should be 0.500 ℏω)
3. Set First Excited preset
4. Note the Expected Energy (should be 1.500 ℏω)
5. Verify the difference is exactly 1.000 ℏω

Experiment B: Count Nodes

1. Set each preset state from n=0 to n=7
2. In Real/Imaginary mode, count the nodes (zero crossings)
3. Verify: State n has exactly n nodes

Experiment C: Observe Coherent State Oscillation

1. Set α = 3 or 4 using the slider
2. Click Coherent State preset
3. Switch to Density/Phase mode
4. Observe the probability oscillating like a classical particle

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Step 10: Record Your Observations

Fill in the observation table below:

S.No	State (n)	Amplitude	Probability |cn|²	Energy En/ℏω
1	n = 0	1	1	0.500
2	n = 1	1	1	1.500
3	n = 2	1	1	2.500
4	n = 3	1	1	3.500
5	n = 4	1	1	4.500
6	n = 5	1	1	5.500
7	n = 6	1	1	6.500
8	n = 7	1	1	7.500

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Quick Actions Reference

Button	Function
🗑️ Zero All	Sets all amplitudes to zero
📐 Normalize	Normalizes wavefunction so Σ|cn|² = 1
🎲 Random	Creates a random superposition
🔄 Reset	Resets simulation to default state
⏸️ Pause/Resume	Stops or continues time evolution

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Tips for Effective Learning

1. Start simple: Begin with single eigenstates before exploring superpositions
2. Compare modes: Switch between Real/Imaginary and Density/Phase to understand both representations
3. Use pause: Freeze the animation to study specific configurations
4. Normalize often: Keep the wavefunction normalized for meaningful probabilities
5. Try extremes: See what happens with very high α values or all states equal