Expectation value of observable

Roughly speaking, an observable is a measurable property of a physical system, such as spin, position, energy, momentum, etc. In terms of Quantum Mechanics, every physical observable corresponds to an operator which acts on the wave function.

Links:

1. Wikipedia.

mean_observable_value

The mean value of the observable operator. See any_quantity.

Symbol:

avg(O)

Latex:

\(\langle O \rangle\)

Dimension:

any_dimension

position

position.

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)

observable

Observable operator as a function of wave_function. See any_quantity.

Symbol:

O(psi)

Latex:

\(O{\left(\psi \right)}\)

Dimension:

any_dimension

law

avg(O) = Integral(conjugate(psi(x, t)) * O(psi(x, t)), (x, -oo, oo))

\[\langle O \rangle = \int \limits_{-\infty}^{\infty} \psi^* (x, t) O[\psi](x, t) dx\]