One-dimensional wave function is normalized¶

For the wave function to be physically acceptable, it needs to be normalized, i.e. the integral of the square of its absolute value must converge to one. The physical meaning of this is that the particle, whose distribution in space is described by the wave function, must exists somewhere in space.

Links:

Physics LibreTexts, formula 3.6.3.

position¶: position in the 1D space.

Symbol:: x
Latex:: \(x\)
Dimension:: length

time¶: time.

Symbol:: t
Latex:: \(t\)
Dimension:: time

wave_function¶: wave_function as a function of position and time.

Symbol:: psi(x, t)
Latex:: \(\psi{\left(x,t \right)}\)
Dimension:: 1/sqrt(length)

normalization_condition¶

Integral(Abs(psi(x, t))^2, (x, -oo, oo)) = 1

Latex:: \[\int\limits_{-\infty}^{\infty} \left|{\psi{\left(x,t \right)}}\right|^{2}\, dx = 1\]