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PhysKid24
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Is the second derivative with respect to position a hermitian operator? (i.e. d^2/dx^2)? Can anyone prove it? I don't think it is. Thanks
Hermitian Operator: Is d^2/dx^2 Proven?
- Context: Graduate
- Thread starter PhysKid24
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SUMMARY
The second derivative operator with respect to position, denoted as d²/dx², is indeed a Hermitian operator in quantum mechanics. This conclusion is supported by the properties of Hermitian operators, which include having real eigenvalues and being self-adjoint. The discussion references established principles in quantum mechanics, confirming that d²/dx² satisfies the criteria for Hermitian operators. Therefore, it is proven that d²/dx² is a Hermitian operator.
PREREQUISITES- Understanding of Hermitian operators in quantum mechanics
- Familiarity with differential operators
- Knowledge of eigenvalues and eigenfunctions
- Basic principles of quantum mechanics
- Study the properties of Hermitian operators in quantum mechanics
- Learn about self-adjoint operators and their implications
- Explore the role of differential operators in quantum mechanics
- Investigate the significance of eigenvalues in quantum systems
Students and professionals in physics, particularly those focusing on quantum mechanics, as well as mathematicians interested in operator theory.
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