Gaussian wavepacket as a solution of the Schrödinger equation

[JorgeM]

Homework Statement

Hello everyone.
I need to find out that the gaussian wavepacket is a solution of the Schrödinger equation.
I first tought that It would be so much easier just to calculate the derivatives and to probe that gaussian equation satisfies Schrodinger's equation but it did not result easy at all.
Do you know any book or place where to find this in the simplest way possible (even the demonstration and not just the probe)
I'm relatively new in studying quantum mechanics so many concepts are new to me.

Relevant Equations

Schrodinger's equation

The Schrödinger equation I need to prove is this one

And the Gaussian wavepacket is found here

Thanks for your advice.

JorgeM

<Moderator's note: upload images to PhysicsForums. Do not use external image servers.>

 

[Abhishek11235]

See:
Introduction to Quantum Mechanics, D.J Griffiths
Quantum Mechanics, N. Zettili

 

[PeroK]

Homework Statement:: Hello everyone.
I need to find out that the gaussian wavepacket is a solution of the Schrödinger equation.
I first tought that It would be so much easier just to calculate the derivatives and to probe that gaussian equation satisfies Schrödinger's equation but it did not result easy at all.
Do you know any book or place where to find this in the simplest way possible (even the demonstration and not just the probe)
I'm relatively new in studying quantum mechanics so many concepts are new to me.
Relevant Equations:: Schrödinger's equation

The Schrödinger equation I need to prove is this one

https://ibb.co/6WMSBH2And the Gaussian wavepacket is found here

https://ibb.co/4RTDRm1Thanks for your advise.

JorgeM

The advice is simple: differentiate!

There is nothing else to do.

PS Welcome to quantum mechanics!

 

[jtbell]

I first tought that It would be so much easier just to calculate the derivatives and to probe that gaussian equation satisfies Schrödinger's equation but it did not result easy at all.

If you show us your work, someone here can probably find where you went wrong.

I strongly suggest that you try to use LaTeX rather than try to post images of your handwritten algebra, because the helpers here find it much easier to read and work with. With LaTeX, people can "quote" indvidual equations or sections of equations in order to highlight errors, which is much more difficult when they're part of an image.

https://www.physicsforums.com/help/latexhelp/

The Gaussian wave packet is one of the more complicated wave functions that you find in an introductory textbook. Have you successfully verified simpler wave functions as solutions to the Schrödinger equation?