Advanced Quantum Mechanics Textbooks: Derivations of Equations

[QuantumWhatNow]

Hi I’m looking for a textbook that shows the derivations of equations such as the different forms of the Schrödinger equation fully and step by step.

 

[Frabjous]

The Schrödinger equation is more motivated than derived. I always liked this discussion.
https://www.physicsforums.com/threads/how-to-derive-schrodingers-equation.1004975/#post-6514138

 

[QuantumWhatNow]

The Schrödinger equation is more motivated than derived. I always liked this discussion.
https://www.physicsforums.com/threads/how-to-derive-schrodingers-equation.1004975/#post-6514138

Thanks. Shocking that book is from 1961. 80 years old! It’s similar to what I am looking for. I’ll provide a bit of context. I’ve accepted the time dependent Schrödinger equation as a fact and starting point. My question, specifically, is how does the time independent equation arise from the time dependent equation. I know you first remove the time component somehow, is that what the linked resource is showing? After I have the time independent I separate it into nuclear and electronic wave function equations by applying the born Oppenheimer approximation. I’ll have a proper look in the morning when I’m at my computer. For even more context i’m a hobby trying to go serious computational chemist.

 

[BvU]

Shocking that book is from 1961. 80 years old!

Funny, I read 1967 and my math finds that 1967 is only 55 years ago

Both careful reading and solid math are very important for computational chemistry

$\$

 

[hutchphd]

I know you first remove the time component somehow, is that what the linked resource is showing? After I have the time independent I separate it into nuclear and electronic wave function equations by applying the born Oppenheimer approximation.

The removal of the time component for solution of the Shrodinger eqn. has very little to do with its genesis. It represents a relatively straightforward (exact) eigenfunction expansion into stationary (persistant in time) states via separation of variables for (manifestly) time independent interactions. Then the fun begins because the number of exact solutions is few but the connection to reality is shockingly diverse.

 

[Demystifier]

Hi I’m looking for a textbook that shows the derivations of equations such as the different forms of the Schrödinger equation fully and step by step.

For step by step presentation I recommend QM Demystified (no, I'm not the author)
https://www.amazon.com/dp/0071765638/?tag=pfamazon01-20

 

[QuantumWhatNow]

Funny, I read 1967 and my math finds that 1967 is only 55 years ago

Both careful reading and solid math are very important for computational chemistry

$\$

Hahaha yes definitely!

 

[QuantumWhatNow]

For step by step presentation I recommend QM Demystified (no, I'm not the author)
https://www.amazon.com/dp/0071765638/?tag=pfamazon01-20

I’ll check it out. It seems like what I’m looking for based on the front cover.

 

[QuantumWhatNow]

The removal of the time component for solution of the Shrodinger eqn. has very little to do with its genesis. It represents a relatively straightforward (exact) eigenfunction expansion into stationary (persistant in time) states via separation of variables for (manifestly) time independent interactions. Then the fun begins because the number of exact solutions is few but the connection to reality is shockingly diverse.

I need to look into eigenfunctions I guess. Not covered that just yet.