Physics · University
Schrodinger equations and a particle in a box · revision notes
The time-dependent equation is iℏ ∂ψ/∂t=Hψ. A time-independent Hamiltonian permits stationary-state analysis.
Key ideas and conditions
Evolution
The time-dependent equation is iℏ ∂ψ/∂t=Hψ. A time-independent Hamiltonian permits stationary-state analysis.
Infinite well
For a nonrelativistic particle in a one-dimensional infinite well of width L, En=n²π²ℏ²/(2mL²), n=1,2,... .
Boundaries
The infinite-well wavefunction vanishes at the walls. Its nonzero ground energy follows from boundary conditions and kinetic-energy structure.
Scaling
Energy scales inversely with mass and L² in this model. Finite wells, interactions and relativistic motion require different treatments.
Explain without looking
- At fixed n and width, mass triples. Find the new energy divided by old energy.
- Give two reasons an electron in a real atom is not accurately represented by an infinite one-dimensional box.
Further reading and review references
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