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Formula Infinite square potential well (1d) Energy    Quantum number    Length   

Formula
Formula: Infinite square potential well (1d)
Energy levels - infinite potential well (1d)
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Energy

Unit
Discrete energy values that a particle can have in the infinite potential well. The energy values are given by the integer quantum number \( n \). For example \(n = 1\):\[ W_{1} ~=~ \frac{h^2}{8m \, L^2} \]

Quantum number

Unit
The quantum number \(n\) takes discrete values: \( n ~=~ 1,2,3... \).

For \( n = 1 \), \( W_1 \) is the ground state energy (also called zero-point energy).

Length

Unit
Length of the one-dimensional potential well.

Mass

Unit
Mass of the particle in the potential well (for example the mass of an electron).

Planck constant

Unit
Planck constant is a natural constant of quantum mechanics and has the value: \( h ~=~ 6.626 \, 070 \, 15 \,\cdot\, 10^{-34} \, \text{Js} \).