Solution to Schrodinger's equation

[Lizwi]

It seems like in University Physics textbook by Young and Freedman,  the SE differential equation is not solved, 

The solution is only predicted and tested. 

Is it not possible to solve it?

[Markus Hanke]

1 hour ago, Lizwi said:

It seems like in University Physics textbook by Young and Freedman,  the SE differential equation is not solved, 

The solution is only predicted and tested. 

Is it not possible to solve it?

Yes, it is of course possible - but only for simple systems, such as various types of simple potential wells, and also for the hydrogen atom. Anything more complex than this generally can’t be done in closed analytical form, which means you need to use numerical methods and computers. Any introductory textbook on quantum mechanics will explain how it is done for simple systems.

[studiot]

I do not know that textbook, but various solutions may be found derived in many Physics and Physical Chemistry textbooks.

Modern Physics by Eisberg

Physical Chemistry by Moore

 

It is important to remember that Schrodinger is a partial differential equation.

As such the boundary conditions are needed to provided any useful solution since general solutions of PDEs involve arbitrary functions.

 

[Markus Hanke]

On 8/9/2020 at 9:16 AM, studiot said:

I do not know that textbook

It is a general introductory textbook for freshmen undergrad students, that gives rough outlines of the major disciplines of physics. It's actually a good book (I have a copy here), since it is very easy to understand due to a large number of illustrations, examples, and exercises. But it's also very basic, and doesn't go in-depth on many topics.

[studiot]

3 hours ago, Markus Hanke said:

It is a general introductory textbook for freshmen undergrad students, that gives rough outlines of the major disciplines of physics. It's actually a good book (I have a copy here), since it is very easy to understand due to a large number of illustrations, examples, and exercises. But it's also very basic, and doesn't go in-depth on many topics.

Well, Liz, there's your answer

Your book is too basic.

Get a more advanced one.

[joigus]

Very good answers you're getting here.

Let's hope crackpottery doesn't make an appearance.

[swansont]

On 8/9/2020 at 3:25 AM, Markus Hanke said:

Yes, it is of course possible - but only for simple systems, such as various types of simple potential wells, and also for the hydrogen atom. Anything more complex than this generally can’t be done in closed analytical form, which means you need to use numerical methods and computers. Any introductory textbook on quantum mechanics will explain how it is done for simple systems.

And, I will add, this is not just true for the Schrödinger equation. In all of physics, there is the tendency to analytically solve only the simplest systems. It’s one reason we tend to look at ideal systems, and ignore complicating factors as much as possible. 

[MigL]

IIRC we didn't get around to solving the Hydrogen atom until 3rd year University Physics.
( after square well, box and harmonic oscillator potentials )

We also did the Helium atom numerically, in 3rd year; using Hollerith punch cards and a Burrows B6700 mainframe computer.
With a printout on fan-fold paper.

Good times.

[uncool]

It's worth noting that the Schrodinger equation isn't really a single system. It's a family of systems. Some simple examples have been solved (as noted); some more complex ones have been numerically approximated by perturbation theory.

So the question doesn't quite make sense; it's kind of like asking "Has A + B = C been solved?"

[Lizwi]

On 8/10/2020 at 3:02 PM, studiot said:

Well, Liz, there's your answer

Your book is too basic.

Get a more advanced one.

Lol, mm, yeah. I get it😂