Two qubits / spins: formalism
Quantum Condensed Matter Physics: Lecture 3
Theoretical physicist Dr Andrew Mitchell presents an advanced undergraduate / introductory Master's level lecture course on Quantum Condensed Matter Physics at University College Dublin. This is a complete and self-contained set of lectures, in which the theory is built up from scratch, and requires only a knowledge of basic quantum mechanics.
In this lecture, I develop the formalism to describe quantum spin systems. We focus on generalizing from one to two spins, the structure of the underlying complex vector spaces, and the corresponding operator algebra. I discuss in detail the concept of basis states, completeness and orthonormality, as well as basis transformations in quantum systems.
Navigate through the lectures of this course in order using the playlist:
• Quantum condensed matt...
Recommended course textbook: "Many-body quantum theory in condensed matter physics" by Bruss and Flensberg.
Пікірлер: 10
You are the best teacher I’ve come across. Kudos!
@drmitchellsphysicschannel2955
3 жыл бұрын
Thank you! I'm glad the lectures are useful!
Thank you, Professor. Your lecture helps me a lot.
Love your teaching styles, really good for beginners. I've been looking for lectures like these for quite some time now. Just wanted to tell you that your courses are really helpful.
@drmitchellsphysicschannel2955
2 жыл бұрын
Thank you! I'm glad the lectures are useful!
Thank you for these great lectures, I finally understood what a basis transformation is.
Does finding U matrices mean we are actually figuring out clebsch gordan coefficients?
At 16:10, the order in the red expression is not switched, but the order in the blue expression is
@drmitchellsphysicschannel2955
Жыл бұрын
The bra in red here is just a definition -- it denotes the adjoint of the corresponding ket. I prefer to keep the order of the indexes the same in bra and ket as a notational convenience. But as we see in blue, the actual order in terms of the direct product of individual vector spaces is reversed in the bra relative to the ket.
@narcosalpha9472
Жыл бұрын
I did not notice that the expression to the left does not have a tensor product, while expression to the right does!! Thank you for your quick clarification, that's amazing!