- #36
adartsesirhc
- 56
- 0
Xezlec, don't despair! Quantum mechanics is a difficult subject to learn for the first time, since it's such a dramatic separation from everything we know so far. Maybe you should try to prepare for QM by learning some more math and physics. I'm learning QM on my own right now, and I eventually want to take Stanford's Education Program for Gifted Youth (EPGY)'s Intro to QM class. Here's the preparation I've had:
Math
1. High school calculus
2. Multivariable and vector calculus
3. Linear algebra
4. A little bit of the calculus of variations
5. A little bit of differential equations - enough to solve first-order and some second-order equations
Physics
1. Mechanics
2. Electricity and magnetism
3. A little bit of intermediate classical mechanics - just Langrangian and Hamiltonian mechanics
I'm using Griffith's Introduction to QM, and I've been doing pretty good. However, there are some bumps in the road occasionally, so I would recommend Stanford's pathway to QM:
Math
1. Multivariable and vector calculus
2. Linear algebra
3. Differential Equations
4. Real analysis
5. Complex analysis
6. Partial differential equations
Physics
1. Mechanics
2. Electricity and magnetism
3. Light and heat
4. Modern physics
5. Intermediate classical mechanics (including the calculus of variations and tensor analysis)
This is probably a much more thorough and complete pathway to QM - all of these courses are required to take EPGY's Introduction to Quantum Mechanics, which is "a rigorous introduction to the theory of quantum mechanics."
Textbook-wise, I would recommend Griffiths as the absolute best for a beginner in QM (and EPGY uses it as the course text), but it does have one drawback - in the introduction, Griffiths talks about the use of mathematics and operators in his book - "My own instinct is to hand the students shovels and tell them to start digging. They may develop blisters at first, but I still think this is the most efficient and exciting way to learn." While this is great for students who want to avoid boring and tedious lectures about the proper use of math and operators, it might not be best for someone who wants to understand the math very well, as you do. Hence, my conclusion: Try Griffiths. If it isn't for you, read Shankar or Sakurai, but be warned - the latter two are usually reserved for graduate classes.
As for your questions, replace every p with the momentum operator, [tex]\frac{\hbar}{i}\frac{\partial}{\partial x}[/tex], and every x with the position operator, [tex]X[/tex]. I don't know what [tex]p_{0}[/tex] and [tex]x_{0}[/tex] are. Then, if you have a function with the operators, use a Taylor series expansion instead. =]
Math
1. High school calculus
2. Multivariable and vector calculus
3. Linear algebra
4. A little bit of the calculus of variations
5. A little bit of differential equations - enough to solve first-order and some second-order equations
Physics
1. Mechanics
2. Electricity and magnetism
3. A little bit of intermediate classical mechanics - just Langrangian and Hamiltonian mechanics
I'm using Griffith's Introduction to QM, and I've been doing pretty good. However, there are some bumps in the road occasionally, so I would recommend Stanford's pathway to QM:
Math
1. Multivariable and vector calculus
2. Linear algebra
3. Differential Equations
4. Real analysis
5. Complex analysis
6. Partial differential equations
Physics
1. Mechanics
2. Electricity and magnetism
3. Light and heat
4. Modern physics
5. Intermediate classical mechanics (including the calculus of variations and tensor analysis)
This is probably a much more thorough and complete pathway to QM - all of these courses are required to take EPGY's Introduction to Quantum Mechanics, which is "a rigorous introduction to the theory of quantum mechanics."
Textbook-wise, I would recommend Griffiths as the absolute best for a beginner in QM (and EPGY uses it as the course text), but it does have one drawback - in the introduction, Griffiths talks about the use of mathematics and operators in his book - "My own instinct is to hand the students shovels and tell them to start digging. They may develop blisters at first, but I still think this is the most efficient and exciting way to learn." While this is great for students who want to avoid boring and tedious lectures about the proper use of math and operators, it might not be best for someone who wants to understand the math very well, as you do. Hence, my conclusion: Try Griffiths. If it isn't for you, read Shankar or Sakurai, but be warned - the latter two are usually reserved for graduate classes.
As for your questions, replace every p with the momentum operator, [tex]\frac{\hbar}{i}\frac{\partial}{\partial x}[/tex], and every x with the position operator, [tex]X[/tex]. I don't know what [tex]p_{0}[/tex] and [tex]x_{0}[/tex] are. Then, if you have a function with the operators, use a Taylor series expansion instead. =]