Question

Show that the energy-time uncertainty principle reduces to the "your name" uncertainty principle (Problem 3.14), when the observable in question is x.

Short answer

The energy-time uncertainty principle reduces to .

Step-by-step solution

The generalized uncertainty principle for two operators.

The generalized uncertainty principle for two operators is:

${\mathit{\delta }}_{\mathbf{A}}^{\mathbf{2}}{\mathit{\delta }}_{\mathbf{B}}^{\mathbf{2}}\mathbf{\ge }{\mathbf{(}\frac{\mathbf{1}}{\mathbf{2}\mathbf{i}}\mathbf{<}\left[\stackrel{⏜}{A},\stackrel{⏜}{B}\right]\mathbf{>}\mathbf{)}}^{\mathbf{2}}$

Show that the energy-time uncertainty principle reduces to the "your name" uncertainty principle.

From the energy-time uncertainty principle, an operator Q satisfies the equation: