Quantum and Atomic Physics Simulators

How to Use

1. Select the quantum system from the dropdown: particle-in-a-box, hydrogen atom, or quantum tunneling scenario
2. Input physical parameters: particle mass (electron = 9.109×10⁻³¹ kg), potential barrier height (eV), well width (nm), and energy level (0-100 eV)
3. Apply the cat-filter to isolate energy eigenstates and visualize probability density distributions across spatial coordinates
4. Run the simulation to compute wave function ψ(x,t) and observe nodal patterns, tunneling probability, or transition frequencies

Worked Example

For an electron in a 1D box of width L=0.5 nm with infinite potential walls: the first three energy levels are E₁=6.04 eV, E₂=24.16 eV, E₃=54.36 eV (using En = n²h²/8mL²). When cat-filter selects n=2, the probability density shows one internal node at x=0.25 nm. For tunneling through a 2 nm barrier with height 5 eV, an electron at 4.5 eV energy gives transmission coefficient T≈0.018 or 1.8% penetration depth.

Practical Notes

1. Use cat-filter to eliminate mixed-state artifacts when analyzing fine structure splitting in alkali atoms above 3000 cm⁻¹ wavenumber ranges
2. For radiation analysis, input Planck constant h=6.626×10⁻³⁴ J·s and fine structure constant α≈1/137 to model photoionization cross-sections in the UV-VUV range (10-200 nm)
3. Verify normalized wave functions sum to unity; tunnel probability scales exponentially as exp(-2κd) where κ=√(2mV₀)/ℏ for barrier penetration predictions in semiconductor heterostructures