QuantumWhatNow
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Hi I’m looking for a textbook that shows the derivations of equations such as the different forms of the schrodinger equation fully and step by step.
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 schrodinger 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.Frabjous said:The Schrodinger equation is more motivated than derived. I always liked this discussion.
https://www.physicsforums.com/threads/how-to-derive-schrodingers-equation.1004975/#post-6514138
Funny, I read 1967 and my math finds that 1967 is only 55 years agoQuantumWhatNow said:Shocking that book is from 1961. 80 years old!
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.QuantumWhatNow said: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.
For step by step presentation I recommend QM Demystified (no, I'm not the author)QuantumWhatNow said:Hi I’m looking for a textbook that shows the derivations of equations such as the different forms of the schrodinger equation fully and step by step.
Hahaha yes definitely!BvU said: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
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I’ll check it out. It seems like what I’m looking for based on the front cover.Demystifier said: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 need to look into eigenfunctions I guess. Not covered that just yet.hutchphd said: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.