Professor M does Science | Tensor product state spaces @ProfessorMdoesScience | Uploaded July 2020 | Updated October 2024, 36 minutes ago.
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📚 State spaces allow us to describe each one of the degrees of freedom of a quantum particle. But what happens when we need to represent several degrees of freedom at the same time, for example three physical dimensions, orbital and spin degrees of freedom, or a system of multiple particles? Tensor product state spaces provide the mathematical tools to study these more complex systems, and in this video we learn how to extend the standard quantities of state spaces to tensor product state spaces. Some systems with multiple degrees of freedom can be described by a trivial combination of the individual components making up the whole system. But quantum mechanics is more interesting than this: some systems cannot be described by a trivial combination of the individual components, and this leads to entangled states.
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⏮️ BACKGROUND
Dirac notation in state space: youtu.be/hJoWM9jf0gU
Operators: youtu.be/pNFna7zZbgE
Representations: youtu.be/rp2k2oR5ZQ8
⏭️ WHAT NEXT?
Eigenvalues and eigenstates in tensor product state spaces: youtu.be/T3ynwXrE0Xw
Identical particles: youtube.com/playlist?list=PL8W2boV7eVfnJ6X1ifa_JuOZ-Nq1BjaWf
Entangled states: [COMING SOON]
~
Director and writer: BM
Producer and designer: MC
💻 Book a 1:1 session: docs.google.com/forms/d/e/1FAIpQLScUL187erItvC7GPnNU2pelsueyVFr94nRq2A5Eq2aVRdGiIQ/viewform?pli=1
📚 State spaces allow us to describe each one of the degrees of freedom of a quantum particle. But what happens when we need to represent several degrees of freedom at the same time, for example three physical dimensions, orbital and spin degrees of freedom, or a system of multiple particles? Tensor product state spaces provide the mathematical tools to study these more complex systems, and in this video we learn how to extend the standard quantities of state spaces to tensor product state spaces. Some systems with multiple degrees of freedom can be described by a trivial combination of the individual components making up the whole system. But quantum mechanics is more interesting than this: some systems cannot be described by a trivial combination of the individual components, and this leads to entangled states.
🐦 Follow me on Twitter: twitter.com/ProfMScience
⏮️ BACKGROUND
Dirac notation in state space: youtu.be/hJoWM9jf0gU
Operators: youtu.be/pNFna7zZbgE
Representations: youtu.be/rp2k2oR5ZQ8
⏭️ WHAT NEXT?
Eigenvalues and eigenstates in tensor product state spaces: youtu.be/T3ynwXrE0Xw
Identical particles: youtube.com/playlist?list=PL8W2boV7eVfnJ6X1ifa_JuOZ-Nq1BjaWf
Entangled states: [COMING SOON]
~
Director and writer: BM
Producer and designer: MC
