Determining uncertanity from the wave equation

[mc_i2020]

Hi!
How does one find out dx and dp from the wave equation?
Appreciate ur help:)

 

[quantumfireball]

the wavefunction in momentum space is the Fourier transform of the wavefunction in position space.
therefore if the wavefunction is spread out in momenta space it is more concentrated in position space and Vice versa
this is just the the property of a function and its Fourier transform.

 

[mc_i2020]

yes I am aware of that but what i asked is how does one find the "uncertainity" in position and momentum FROM the wave eqn?

 

[ZapperZ]

yes I am aware of that but what i asked is how does one find the "uncertainity" in position and momentum FROM the wave eqn?

I'm assuming you meant the wave function rather than the wave equation. Wave equation usually refers to the differential equation, while the wave function is a solution to the wave equation.

It is difficult to answer your question because you did not reveal what you already know. Have you taken basic QM before?

For example, to get the value for $\Delta x$ from the wavefunction, you have to know the definition of it, which is

$$\Delta x = \sqrt{<x^2> - <x>^2}$$

where

$$<x^2> = <\psi|x^2|\psi>$$

etc, and $\psi$ is the wave function.

So that's how you get $\Delta x$ knowing the wavefunction. Similarly for the momentum.

Zz.