The ground state energy of an electron in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls ?

Is independent of temperature

Is zero

Decreases with temperature

Increases with temperature

Explanation

In quantum mechanics, an electron in a one-dimensional infinite potential well (also called a "quantum box" or "particle in a box") has discrete energy levels given by:

$E_n = frac{n^2 h^2}{8mL^2}$ 8mL^2

Where:

$n$ = quantum number (for ground state $n = 1$ )
$h$ = Planck’s constant
$m$ = mass of the electron
$L$ = width of the box

▶ These energy levels depend only on the physical parameters (like mass, size of the box), not on temperature.

The ground state energy (lowest possible energy) is:

$E_{1} = h^ ^{2/}$ 8mL^2