Calculate Quantum Energy Levels with Precision
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Calculate energy levels for a particle in a one-dimensional box.
Calculate the de Broglie wavelength for the particle.
The particle in a box model is a fundamental quantum mechanical system that describes a particle confined to move in a one-dimensional box with infinitely high walls. This simple model demonstrates key quantum mechanical concepts like energy quantization and wave-particle duality.
The energy levels in a particle in a box are quantized according to:
En = (n²h²)/(8mL²)
where:
The wavefunction for a particle in a box is:
ψn(x) = √(2/L)sin(nπx/L)
This describes the probability amplitude of finding the particle at position x.
The particle in a box model is used to understand:
En = (n²h²)/(8mL²)
λ = h/√(2mE)
|ψ(x)|² = (2/L)sin²(nπx/L)