How to show that expectation value is always positive?

[ngkamsengpeter]

Homework Statement

In quantum mechanics, how to show that the expectation value is always positive?

Homework Equations

The Attempt at a Solution

 

[CompuChip]

Can you be more specific? Because as you stated it, one can easily find a counter-example (e.g. <x> for a Gaussian wavepacket centered at some x₀ < 0).

 

[ngkamsengpeter]

Can you be more specific? Because as you stated it, one can easily find a counter-example (e.g. <x> for a Gaussian wavepacket centered at some x₀ < 0).

Questions just tell us to show that A⁺A is always self-adjoin and then show that expectation is non-negative.