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Finite potential well
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Wavefunctions leak into walls.
ψ penetrates into the classically forbidden walls, giving lower energies than the infinite well and a finite number of bound states.
Quantum wells in semiconductor lasers.
Always at least one bound state in 1D.
In more detail
In a finite potential well, a particle has bound states with finite walls, and some probability leaks into the classically forbidden region. There are a limited number of bound states, depending on the well depth.
Real-world uses
- Quantum well lasers use finite well structures.
- Semiconductor heterostructures are designed with finite wells.
- Quantum engineers study finite wells to model electrons in semiconductor heterostructures.
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Frequently asked questions
Why does the wavefunction extend outside?
Because quantum wavefunctions decay gradually into the walls rather than stopping sharply.
How many bound states are there?
It depends on the well depth and width, with deeper wells having more states.
Can a particle exist in the walls?
Yes, in quantum mechanics the wavefunction leaks into the barrier, where it decays but does not become zero.
Related topics in Quantum Mechanics
Commutators · Particle in a box · Free particle · Quantum tunnelling · Tunnelling applications · Alpha decay as tunnelling