Learn Quantum Mechanics with Free Hilbert Space Courses

In summary, the conversation discusses the search for a good online course on the mathematical background of quantum mechanics. The speaker expresses difficulty in finding a course that makes the distinction between Hermitian and self-adjoint operators, but acknowledges that this may not be necessary for introductory courses. They also mention a university in Belgrade that offers a condensed crash course on Hilbert spaces and suggests trying to access their translated courses.
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dextercioby
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...For abut two weeks I've searching the internet for a good online (i.e.free for download)course on the basis of quantum mechanics,that means the mathematical background of this theory.I found a few,especially from American colleges,but all of them seemed to have serious problems regarding mathematical and logcal coherence.I mean all of them do not make the distinction between hermitic and self adjoint operators(and it's obviously not all).
I find this distinction to be of some relevance in quantum mechanics,don't you?
 
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  • #2
Originally posted by dextercioby
...For abut two weeks I've searching the internet for a good online (i.e.free for download)course on the basis of quantum mechanics,that means the mathematical background of this theory.I found a few,especially from American colleges,but all of them seemed to have serious problems regarding mathematical and logcal coherence.I mean all of them do not make the distinction between hermitic and self adjoint operators(and it's obviously not all).
I find this distinction to be of some relevance in quantum mechanics,don't you?

Yes and no. It's Hermitian, BTW. The difference is not noticable in the stuff you do in introductory QM and most intro courses don't want to swamp the students in fancy dan Hilbert space / C*-algebra / functional analysis stuff, that requires almost a full unit in itself to get really up to speed. I'd say go with the flow, keeping in mind that there is a difference and it will be time enough for you to bring your knowledge of that to bear after you are skilled with the basics.
 
  • #3
Heh, unfortunately, there are some places on the Earth that do not wish to follow the mainstream. Students of physics in Belgrade
do have the pleasure to meet Hilbert spaces in all their complexity in a super-condensed one semestre crash course at undergrad level.
I know that this faculty(www.ff.bg.ac.yu[/URL]) has some courses already translated in English, so you could give it a try. They, definitely have an online pdf text on Hilbert spaces, however it is in Serbian. ;-)
 
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1. What is quantum mechanics?

Quantum mechanics is a branch of physics that deals with the behavior of matter and energy at a very small scale, such as atoms and subatomic particles. It explains how particles behave and interact with each other on a quantum level, which is drastically different from the classical mechanics that governs larger objects.

2. What is Hilbert space?

Hilbert space is a mathematical concept that is used to describe the state of a quantum system. It is a complex vector space that allows for the superposition of multiple states, which is a fundamental principle of quantum mechanics. Hilbert space is used to make calculations and predictions about the behavior of quantum systems.

3. Why is it important to learn quantum mechanics?

Quantum mechanics is crucial for understanding the fundamental nature of matter and the universe. It has led to groundbreaking discoveries and technologies such as transistors, lasers, and computer memory. Additionally, many modern technologies, such as quantum computing, rely on the principles of quantum mechanics.

4. Are there any free courses available to learn quantum mechanics?

Yes, there are many free online courses available to learn quantum mechanics, including courses that specifically focus on Hilbert space. These courses are offered by universities, organizations, and individuals and can be found on platforms such as Coursera, edX, and YouTube.

5. Do I need a background in math to learn quantum mechanics?

While a basic understanding of math is helpful, it is not necessary to have a strong mathematical background to learn quantum mechanics. Many introductory courses start with the basics and build up the necessary math skills as you progress through the course. However, some familiarity with concepts such as calculus and linear algebra can be beneficial.

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