⭐ When you enter the simulation section, a guided tour will appear. It is strongly recommended that you take the tour for the first time, as it provides step-by-step instructions to help you understand the experiment thoroughly. The tour also introduces you to the various controls, features, and interface elements, making it easier for you to navigate and explore the experiment effectively.

Task-1: Quantum Wavefunction Visualization and Potential Type Identification

In the first task, the user is presented with quantum wavefunction visualizations showing different potential configurations. The simulation displays:

• Two wavefunction plots with different potential shapes labeled "infinite well" and "harmonic oscillator"
• Energy eigenstate solutions showing distinct probability density distributions
• Quantum number dependencies with different n-values for each potential type
• Interactive 3D visualization of wavefunction evolution and probability clouds

The user must identify and label each wavefunction with their respective potential type and explain how boundary conditions affect the quantum states and energy levels.

Task-2: Interactive Parameter Effects on Quantum States

In the second task, there are interactive controls showing how quantum parameters affect wavefunction properties where users can observe:

• Energy Level Adjustment: Modify quantum energy from 0.1-5.0 eV to see eigenstate changes
• Potential Width Control: Vary potential well width to study confinement effects
• Potential Depth Variation: Adjust potential barrier height to observe bound state formation
• Quantum Number Selection: Change principal quantum numbers to explore different eigenstates

Real-time wavefunction updates allow users to understand the relationship between potential parameters, boundary conditions, and resulting quantum mechanical solutions.

Task-3: Wavefunction Properties and Measurement Analysis

In the third task, users explore quantum measurement concepts through:

• Probability Density Visualization: Toggle between wavefunction amplitude and probability density views
• Position Uncertainty: Measure position spreads and uncertainty principle demonstrations
• Momentum Distribution: Analyze momentum space representations and Fourier transforms
• Energy Eigenvalue Calculation: Study energy quantization and level spacing

Interactive draggers allow real-time parameter adjustment with immediate feedback on quantum mechanical properties and measurement outcomes.

Task-4: Quantum Tunneling and Barrier Penetration

In the fourth task, the simulation demonstrates quantum tunneling phenomena with:

• Barrier Transmission: Visualize wavefunction penetration through potential barriers
• Tunneling Probability: Calculate transmission coefficients for different barrier configurations
• Wave Packet Dynamics: Observe time evolution of quantum wave packets approaching barriers
• Reflection Coefficients: Study partial reflection and transmission at potential discontinuities

Users can adjust barrier parameters and observe how quantum particles exhibit wave-like behavior in classically forbidden regions.

Task-5: Interactive Challenge Assessment System

The fifth task provides comprehensive assessment through multiple challenge formats:

Challenge 1: Rapid Fire Quiz

• Quantum mechanics fundamentals and wavefunction interpretation
• Energy eigenvalue identification and quantum number relationships
• Probability density analysis and measurement principles
• Potential type recognition and boundary condition effects

Challenge 2: Fill-in-the-Blanks

• Complete statements about Schrödinger equation solutions and quantum states
• Calculate key parameters like energy levels, wavelengths, and probability densities
• Identify quantum mechanical operators and their physical meanings

Challenge 3: Matching Exercise

• Match potential shapes with their corresponding wavefunction solutions
• Connect quantum numbers with their associated energy levels and spatial distributions
• Associate measurement outcomes with appropriate quantum mechanical concepts

Challenge 4: Advanced Calculations

• Perform quantitative analysis using time-independent Schrödinger equation
• Calculate tunneling probabilities using WKB approximation methods
• Determine expectation values for position, momentum, and energy operators