QM · Ch 2 · Infinite square well energies
Physics · Quantum Mechanics · Griffiths Ch 2
Problem
A particle of mass is confined to the 1D infinite square well for and otherwise. (a) Solve the TISE for the stationary states and find . (b) Write the ground-state energy. (c) Where is the particle most likely to be found in the ground state?Intuitive explanation
The infinite square well is the simplest quantum system where boundary conditions force quantization. Inside the well, the particle behaves like a free particle, but the hard walls at and require the wavefunction to vanish there—this constraint allows only discrete wavelengths to fit, each with its own energy. Solving the time-independent Schrödinger equation and applying these boundary conditions will give you both the allowed energies and the shape of each stationary state.
Intuitive explanation
The infinite square well is the simplest quantum system where boundary conditions force quantization. Inside the well, the particle behaves like a free particle, but the hard walls at and require the wavefunction to vanish there—this constraint allows only discrete wavelengths to fit, each with its own energy. Solving the time-independent Schrödinger equation and applying these boundary conditions will give you both the allowed energies and the shape of each stationary state.