Quantum Advanced Quantum Mechanics Textbooks: Derivations of Equations

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The discussion focuses on finding a textbook that provides detailed, step-by-step derivations of the Schrödinger equation, particularly how the time-independent equation emerges from the time-dependent version. The participants note that the time-dependent Schrödinger equation is often accepted as a starting point, with the removal of the time component being a key step in deriving the time-independent equation. This process involves a straightforward eigenfunction expansion into stationary states, which is crucial for understanding quantum mechanics. Recommendations include the book "QM Demystified" for its clear presentation of these concepts. The importance of careful reading and solid mathematical foundations in computational chemistry is also emphasized, alongside the need to explore eigenfunctions for a deeper understanding.
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.
 
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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
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.
 
QuantumWhatNow said:
Shocking that book is from 1961. 80 years old!
Funny, I read 1967 and my math finds that 1967 is only 55 years ago :smile:

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

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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.
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.
 
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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.
For step by step presentation I recommend QM Demystified (no, I'm not the author)
https://www.amazon.com/dp/0071765638/?tag=pfamazon01-20
 
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BvU said:
Funny, I read 1967 and my math finds that 1967 is only 55 years ago :smile:

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

##\ ##
Hahaha yes definitely!
 
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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.
I need to look into eigenfunctions I guess. Not covered that just yet.
 
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