# Simulation of Quantum Tunneling Gaming Project in C++

### Explanation

1. Constants:
• PI: Mathematical constant π.
• HBAR: Reduced Planck’s constant (h/2π), crucial for quantum mechanics calculations.
• MASS: Mass of an electron (in kilograms), used for wave function calculations.
2. Function `waveFunction(double x, double potential, double energy, double width)`:
• Purpose: Computes the wave function of a particle given a potential barrier and energy.
• Parameters:
• `x`: Position where the wave function is evaluated.
• `potential`: Height of the potential barrier.
• `energy`: Energy of the particle.
• `width`: Width of the potential barrier.
• Implementation:
• Calculates wave numbers `k` and `kappa` based on the potential and energy.
• Applies different formulas for the wave function inside and outside the potential barrier.
• Returns the computed wave function value.
3. Function `simulateQuantumTunneling(double potential, double energy, double width, int numPoints)`:
• Purpose: Simulates and prints the quantum tunneling effect across a range of positions.
• Parameters:
• `potential`: Height of the potential barrier.
• `energy`: Energy of the particle.
• `width`: Width of the potential barrier.
• `numPoints`: Number of discrete points to compute and display.
• Implementation:
• Computes positions and corresponding wave functions using the `waveFunction` function.
• Prints the results in a tabulated format.
4. Main Function:
• Setup: Defines parameters for potential, energy, width of the barrier, and number of points for simulation.
• Simulation: Calls `simulateQuantumTunneling` to compute and display the wave function over a range of positions.

### Usage

• Quantum Tunneling Simulation: Provides a basic simulation of quantum tunneling through a potential barrier.
• Wave Function Visualization: Helps visualize how the wave function of a particle changes as it interacts with a potential barrier.
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