How to gain an understanding of the Schrodinger equation for a noob

[CrimpJiggler]

Should I start by learning about the equations for classical harmonic waves and how the de Brolier equations can be applied to them? What else should I learn? I'm a chemistry student and we did a class on quantum chemistry, but the mathematical side of it was way too complicated for me so I just relied on visual exam questions to pass the class (Maths isn't my strong point but visual thinking is) but I am now working on computational chemistry related things and I want to gain a good understanding of the Schrödinger equation.

 

[VantagePoint72]

The de Broglie equations aren't applied to waves, they're applied to particles. That's the point: given a particle with a particular momentum, you determine the corresponding wave. However, the mechanics of classical waves will be helpful for understanding the solutions to the Schrödinger equation. Once you've done that, the introductory QM book by David Griffiths is nice for first contact with the theory.

 

[wotanub]

You basically need to know these things, in roughly this order:
*What is a differential equation
*What is a quantum state vector
*What is an operator, and how do I use it
*How do I solve eigenvalue problems
*How do states evolve with time in quantum mechanics
*What is the Schrödinger equation

Start off by improving your math and try to learn QM from the perspective of matrix mechanics. Wave mechanics is usually taught first, but in my experience, it doesn't click as well as matrix mechanics for a first timer. My recommended book is the one by Townsend.

 

[gadong]

You basically need to know these things, in roughly this order:
*What is a differential equation
*What is a quantum state vector
*What is an operator, and how do I use it
*How do I solve eigenvalue problems
*How do states evolve with time in quantum mechanics
*What is the Schrödinger equation

Start off by improving your math and try to learn QM from the perspective of matrix mechanics. Wave mechanics is usually taught first, but in my experience, it doesn't click as well as matrix mechanics for a first timer. My recommended book is the one by Townsend.

Forget about matrix mechanics and quantum state vectors - you need a book on computational chemistry (e.g. Computational Quantum Chemistry by Alan Hinchliffe). Physicists do things differently, with more rigour than chemists need, on the fundamentals.

 

[VantagePoint72]

Forget about matrix mechanics and quantum state vectors - you need a book on computational chemistry (e.g. Computational Quantum Chemistry by Alan Hinchliffe). Physicists do things differently, with more rigour than chemists need, on the fundamentals.

Learn math from mathematicians, physics from physicists, and chemistry from chemists. QM geared for chemistry is perfectly sufficient for computational purposes; however, since OP said he/she wants to "gain an understanding" of it then it needs to be learned in its proper context: a fundamental theory of physics.

 

[DimReg]

I feel like if you are doing computational work, there is no getting around understanding the math.

The Schrödinger equation is a differential equation, which relates a function to one or more of it's derivatives. Actually, it's a partial differential equation, which means it relates a function to one or more of it's partial derivatives. Because one of these partial derivatives is time, the Schrödinger equation tells you how the function evolves with time.

So what is this function it tells you about? It's the wavefunction, which encodes all the information about the particle you are modelling. Exactly how to think about the wavefunction is probably best left for a textbook, but basically everything you want to calculate about a quantum particle is done using the wavefunction.

Actually, there are lots of situations where the Schrödinger equation is not very complicated. Try looking up the Infinite Square well. Also look up finite step potentials. These two systems are simple enough that they shouldn't tax your math skills too much.

 

[gadong]

Quantum chemistry and quantum physics are different subjects with different goals.

 

[cytochrome]

Should I start by learning about the equations for classical harmonic waves and how the de Brolier equations can be applied to them? What else should I learn? I'm a chemistry student and we did a class on quantum chemistry, but the mathematical side of it was way too complicated for me so I just relied on visual exam questions to pass the class (Maths isn't my strong point but visual thinking is) but I am now working on computational chemistry related things and I want to gain a good understanding of the Schrödinger equation.

I would definitely get a good understanding of classical harmonics because it can allow for an intuitive feel of how the solutions are acting. Having a firm understanding of differential equations is a must so you can also know where the solutions come from and how they are basically the same for the Schrödinger equation and other wave equations. I took a course on classical mechanics (upper level physics, not physics 1) and modern optics and I feel these two courses set me up very well to understand the nature of the Schrödinger equation.

 

[cgk]

Quantum chemistry and quantum physics are different subjects with different goals.

No, they are not. Quantum chemistry *is* applied quantum mechanics. In fact, quantum chemsitry goes *WAY* deeper into technicalities, many-body formalisms, and math than a typical quantum mechanics course. QC currently has the most powerful many-body methods found anywhere in physics! The reason for this is that in quantum chemsity, you actually need to calculate numbers, and this requires a deep in sight into how all the quantum theory works and plays together.

To OP: I am sorry to say that, but if you really cannot get comfortable with the math, then computational chemistry is not for you. This is not about understanding the Schroedinger equation. The Schroedinger equation is step 1 of 20000. In order to do good quantum chemistry, you also need to have an in-depth knowledge of all the many-body theory, approximation methods (and their limits of applicability), technicalities (which program can do what and why?) and countless arcane details about special systems.