Скачать или смотреть What is a Hermitian Operator? Hermitian Conjugate & Properties of Hermitian Operators

What are Hermitian Operators in Quantum Mechanics? In this video I discuss Hermitian Adjoint (or Conjugate) and the various important properties (theorems) of Hermitian Operators.

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   • Quantum Mechanics  

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𓏬𓏬𓏬𓏬𓏬VIDEO DESCRIPTION𓏬𓏬𓏬𓏬𓏬𓏬
Hermitian operators represent physical observables (like energy, momentum, spin) in quantum mechanics. The defining feature of a Hermitian operator is that its measured values, or eigenvalues, are always real numbers—reflecting the reality of measurable physical quantities. They have the following key properties:
1. Real eigenvalues (ensuring measurable outcomes are real)
2. Orthogonal eigenstates (distinct outcomes correspond to orthogonal states)
3. Complete eigen-basis (any state can be expressed using their eigenstates)
Hermitian operators provide the essential bridge between theory and measurement in quantum mechanics.

In this video, I discuss the definition, properties and consequences of Hermitian adjoin (or hermitian conjugate) and Hermitian Operators.

00:00 Hermitian Operators
04:28 Hermitian Adjoint
11:31 Properties of Hermitian Operators
30:28 Is d/dx a Hermitian Operator?
38:36 Is d2/dx2 a Hermitian Operator?
42:00 Skew Hermitian Operator


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