# Formula Infinite Square Potential Well (1d) Energy Quantum number Length

## Energy

`$$ W_n $$`Unit

`$$ \mathrm{J} $$`

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

`$$ n $$`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

`$$ L $$`Unit

`$$ \mathrm{m} $$`

Length of the one-dimensional potential well.

## Mass

`$$ m $$`Unit

`$$ \mathrm{kg} $$`

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

## Planck's Constant

`$$ h $$`Unit

`$$ \mathrm{Js} = \frac{ \mathrm{kg} \, \mathrm{m}^2 }{ \mathrm{s} } $$`

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