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Kiki
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What are strong graduate programs for researching foundations of quantum mechanics?
Dishsoap said:What do you mean? The foundations of quantum mechanics are pretty well established.
The stuff people argue about incessantly in our Quantum Physics forum? (Interpretations; Bell's Theorem and related things)Dishsoap said:What do you mean?
jtbell said:The stuff people argue about incessantly in our Quantum Physics forum?
I would love to read about such notions. Although google might help me out, but what references do you recommend?micromass said:Those silly discussions are about interpretations, which is foundations too of course. But there is other stuff. For example, you can do projective geometry and its relation to quantum mechanics, or you can do the C*-algebraic approach to quantum theory. Those are all very interesting foundational stuff that don't go into interpretations.
Ravi Mohan said:I would love to read about such notions. Although google might help me out, but what references do you recommend?
(Sorry for hijacking but I really find this interesting). I am a graduate student at UT Austin and my field of research is String Theory. In mathematics, I am quite familiar with rigged Hilbert Space formalism, differential geometry, topology and algebra. In physics I am comfortable with quantum mechanics, quantum field theory and general relativity (coordinate dependent/independent formalisms). I have taken graduate courses in physics topics I mentioned.micromass said:If you tell me the math and physics you're comfortable with, I might be able to give you a quick introductin to thee books.
Ravi Mohan said:(Sorry for hijacking but I really find this interesting). I am a graduate student at UT Austin and my field of research is String Theory. In mathematics, I am quite familiar with rigged Hilbert Space formalism, differential geometry, topology and algebra. In physics I am comfortable with quantum mechanics (had 2 graduate courses in it), quantum field theory and general relativity (coordinate dependent/independent formalisms).
micromass said:Anyway, Strocchi starts off immediately with the C*-algebraic approach. The idea is to make operators/observables the primary object of QM, and not the states. This results in a very natural approach to quantum mechanics. You basically see that QM is the exact same thing as classical mechanics, but only "made noncommutative". The usual Hilbert space formalism (and the rigged Hilbert space formalism actually) can be derived from the more natural C*-algebraic formalism. This is known as the Gelfand-Naimark-Segal construction.
micromass said:As for quantum logic. The idea is that observables in QM are measurable functions to the Borel sigma-algebra of the reals. Quantum logic then approaches the subject by replacing this measurable function/sigma algebra by a more general structure. This structure essentially is projective geometry, which is quite surprising.
In Hall, quantum mechanics is derived from scratch but rigorously. Functional analysis is applied rigorously to the theory.
The Graduate Program in QM focuses on researching the foundations of quantum mechanics. This includes studying the fundamental principles and theories of quantum mechanics, as well as exploring its applications in various fields such as physics, chemistry, and engineering.
Any student who has completed a bachelor's degree in a related field, such as physics, mathematics, or engineering, is eligible to apply for the Graduate Program in QM. However, admission is highly competitive and may also require strong academic performance and letters of recommendation.
The Graduate Program in QM covers a wide range of research topics, including quantum information, quantum computing, quantum optics, and quantum field theory. Students may also have the opportunity to conduct research in collaboration with faculty members and participate in cutting-edge experiments.
Graduates of the Graduate Program in QM have a range of career opportunities in both academia and industry. Many go on to pursue careers as research scientists, professors, or engineers in fields such as quantum computing, quantum cryptography, and quantum materials. Others may also find opportunities in government agencies or national laboratories.
Yes, the Graduate Program in QM offers the flexibility for students to specialize in a specific area of quantum mechanics based on their research interests. Students can work closely with faculty members to design a program of study that aligns with their career goals and research interests.