Advanced Quantum Mechanics Textbooks: Derivations of Equations

In summary, the book QM Demystified is a good resource for step by step derivations of the different forms of the schrodinger equation.
  • #1
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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  • #3
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.
 
  • #4
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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  • #5
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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  • #6
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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  • #7
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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  • #8
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  • #9
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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1. What is the purpose of studying advanced quantum mechanics textbooks?

The purpose of studying advanced quantum mechanics textbooks is to gain a deeper understanding of the fundamental principles and mathematical framework of quantum mechanics. This knowledge is essential for those pursuing careers in fields such as physics, chemistry, and engineering, where quantum mechanics plays a crucial role.

2. How are equations derived in advanced quantum mechanics textbooks?

Equations in advanced quantum mechanics textbooks are derived using mathematical techniques such as linear algebra, calculus, and differential equations. These derivations involve applying the fundamental principles of quantum mechanics, such as the Schrödinger equation, to various physical systems and scenarios.

3. Are advanced quantum mechanics textbooks suitable for beginners?

No, advanced quantum mechanics textbooks are not suitable for beginners. They assume a strong foundation in mathematics, physics, and basic quantum mechanics principles. It is recommended to have a solid understanding of introductory quantum mechanics before attempting to study advanced textbooks.

4. How can one effectively study from advanced quantum mechanics textbooks?

To effectively study from advanced quantum mechanics textbooks, it is important to have a thorough understanding of the basic principles and equations of quantum mechanics. It is also helpful to have a strong background in mathematics, particularly linear algebra and calculus. Regular practice and solving problems are also essential for mastering the material.

5. What are some popular advanced quantum mechanics textbooks?

Some popular advanced quantum mechanics textbooks include "Principles of Quantum Mechanics" by R. Shankar, "Quantum Mechanics: Concepts and Applications" by N. Zettili, and "Quantum Mechanics" by D. J. Griffiths. These textbooks are widely used in universities and are known for their clear explanations and comprehensive coverage of the subject.

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