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Suggestions on Getting Good at Quantum Formalism

Anonymous Thu 05 Sep 18:05:17 2019 No.10946665 View Reply Original Report

Quoted By: >>10946699 >>10947680 >>10947684 >>10948299

Hey all,
So I'm a senior about to finish my B.S. in physics, taking our university's 2nd level of quantum. I really need help learning the formalism of not only the linear algebra, but the actual physics. I get bogged down when the textbooks jump between the operator formalism and the wave-function formalism.

Does anyone have any good books, videos, or any other resource that can help with this?

Anonymous

Anonymous Thu 05 Sep 2019 18:07:46 No.10946668 Report

Quoted By: >>10946678

wat book you using?

Anonymous

Anonymous Thu 05 Sep 2019 18:11:48 No.10946678 Report

Quoted By: >>10948296

>>10946668
Griffiths for the class but I recently started looking at Zettili. In both books, as well as my professor, they constantly jump between wave function formalism and state vector formalism. This confuses and annoys me. Maybe it's because I don't have solid grasp of the mathematics, but I hope someone can simply explain the reasoning for this.

Anonymous

Anonymous Thu 05 Sep 2019 18:19:58 No.10946699 Report

Quoted By:

>>10946665
Libgen.is
Search Dirac The Principles of Quantum Mechanics.

This is from classic mechanics to Quantum mechanics.

John von Neumann
Mathematical Foundations of Quantum Mechanics.

Quantum formalism using Hilbert space and join dirac particle matrix mechanics and Schrödinger wave equation.

Introductory functional analysis with applications
Erwin Kreyszig

Full Explain functional Analysis with modern terms and only need calculus and linear algebra as background, last chapter show Schrödinger Equation using functional analysis.

Anonymous

Anonymous Thu 05 Sep 2019 21:06:00 No.10947080 Report

Quoted By:

Watch Fredrick Schuller's lecture on QM on YouTube. Its a first year grad class, and he develops it very cleanly with a lot of attention paid to mathematical precision.

Anonymous

Anonymous Fri 06 Sep 2019 01:33:42 No.10947680 Report

Quoted By:

>>10946665
You dumb I'm reading out of Schrodinger's papers and I'm Community College Dropout for something else

Anonymous

Anonymous Fri 06 Sep 2019 01:36:26 No.10947684 Report

Quoted By: >>10947689

>>10946665
I bet you my goddamn soul I propose an experiment before you do

Anonymous

Anonymous Fri 06 Sep 2019 01:37:42 No.10947689 Report

Quoted By:

>>10947684
In fact in this is a CC drop out for something else here I've proposed 250,000* 250000 X whatever experiments novel experiments Plus dare I say 250000 times 250000

Anonymous

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Anonymous Fri 06 Sep 2019 05:58:35 No.10948296 Report

Quoted By: >>10948300

>>10946678
The vector and operator notation (I'm assuming it is bra-ket?) is better suited for abstractly understanding what is happening. For example, in this notation the possible energy states of a quantum mechanical object are the eigenvectors (technically eigenfunctions) of the Hamiltonian operator, with eigenvalues being the energy of the system. In this formalism, it is easier to see the connection of QM to classical physics. The Hamiltonian operator takes the form of: $\frac{P^{2}}{2m}+V$
where P is the momentum operator and V is what I am using to represent the operators giving the potential energy. This should remind you of the Hamiltonian of a classical system (since the first part is kinetic energy).

This abstract formulation will go into the wavefunction notation (i.e., as a differential equation and polynomial notations) when you go into a basis. There arr multiple bases quantum mechanics can take place in, you can look at the wavefunctions for the position of a particle and the wavefunctions for its momentum. These are given by the same equation in the abstract operator notation. However, in different bases abstract operators take different forms, for example the momentum operator goes to $-ih\<br />pderivative{x}$ , which when plugged into the abstract equation yields differential equation expression of the wavefunction.

The polynomial functions are actually elements in a vector space, hence why they are represented by vectors in the vector notation.

I'd reccomend Shankar for extra reading, it is a graduate text but explains these things better.

Anonymous

Anonymous Fri 06 Sep 2019 05:59:32 No.10948299 Report

Quoted By:

>>10946665
https://www.youtube.com/watch?v=JL88omsU5dU

Anonymous

Anonymous Fri 06 Sep 2019 06:00:57 No.10948300 Report

Quoted By:

>>10948296
Second equation should be $-ih \pdv{x}$
unless /sci/ can't LaTeX.

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