Professor M does Science | Functions of operators in quantum mechanics @ProfessorMdoesScience | Uploaded May 2021 | Updated October 2024, 10 minutes ago.
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📚 Many important phenomena in quantum mechanics are described by functions of operators. For example, spatial translations are given by an exponential function of the momentum operator, and time evolution is given by an exponential function of the Hamiltonian. In this video we explain how to construct the function of an operator, and explore what their properties are.

⏮️ BACKGROUND
State space and dual space: youtu.be/hJoWM9jf0gU
Operators: youtu.be/pNFna7zZbgE
Adjoint operator: youtu.be/b_DcsVCtP5I
Commutator algebra: youtu.be/57xgSIV9PY0
Eigenvalues and eigenstates: youtu.be/p1zg-c1nvwQ

⏭️ WHAT NEXT?
Hermitian operators: youtu.be/XIgDUfyrLAY
Unitary operators: youtu.be/baIT6HaaYuQ
Translation operators: youtu.be/978mMgGYs1M
Time evolution operator: youtu.be/zqmU4dW03aM

📖 READ MORE
If you are interested in the mathematics behind the Baker-Campbell-Hausdorff formula, further details can be found in the following links:
* http://webhome.phy.duke.edu/~mehen/760/ProblemSets/BCH.pdf
* http://math.columbia.edu/~rzhang/files/BCHFormula.pdf

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Director and writer: BM
Producer and designer: MC