Professor M does Science | 2-state quantum systems: energy eigenstates @ProfessorMdoesScience | Uploaded October 2023 | Updated October 2024, 12 minutes ago.
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📚 2-state quantum systems are key to understand phenomena ranging from the spin angular momentum of electrons and protons to the qubits of quantum computers. In this video, we calculate the energy eigenstates of a 2-state quantum system.

0:00 Introduction
3:08 The "d dot sigma" operator
8:21 Eigenvalues of the "d dot sigma" operator
11:17 Eigenstates of the "d dot sigma" operator
15:00 Energy eigenstates
20:15 Wrap-up

⏮️ BACKGROUND
Pauli matrices: youtu.be/2MsVD9ufguk
2x2 matrix space: youtu.be/OdYNKLULvlU
Two-state quantum systems | Eigenvalues: youtu.be/kQnQpI2B72s
Operators: youtu.be/pNFna7zZbgE
Matrix formulation: youtu.be/wIwnb1ldYTI
Hermitian operators: youtu.be/XIgDUfyrLAY
Eigenvalues and eigenstates: youtu.be/p1zg-c1nvwQ

⏭️ WHAT NEXT?
Spin 1/2: [COMING SOON]
Rabi oscillations: [COMING SOON]

🧮 Double angle formulae
Wikipedia: en.wikipedia.org/wiki/List_of_trigonometric_identities#Double-angle_formulae
Wolfram MathWorld: mathworld.wolfram.com/Double-AngleFormulas.html

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Director and writer: BM
Producer and designer: MC