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astrozilla
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Homework Statement
How can we compute the error or uncertainty in measuring an operator O ?
astrozilla said:This is definitely a very stupid exam question.
I just thought that there is some mathematical formula or that ΔO (uncertainty) is related somehow to Werner Heisenberg's uncertainty principle.
A quantum mechanics operator is a mathematical representation of a physical observable in the quantum mechanical system. It acts on the wave function of a particle and provides information about the observable's value.
Quantum mechanics operators are used in calculations to determine the expected values of physical observables, such as position, momentum, and energy, in a quantum mechanical system. They are also used to calculate the probability of obtaining a certain measurement value for a given observable.
A Hermitian operator is self-adjoint, meaning its eigenvalues are real and its eigenvectors are orthogonal. This allows for easier interpretation and calculation of physical observables. Non-Hermitian operators, on the other hand, do not satisfy these properties and may have complex eigenvalues and non-orthogonal eigenvectors.
Yes, quantum mechanics operators can be represented by matrices. In fact, the mathematical formalism of quantum mechanics uses linear algebra and the representation of operators as matrices to describe the behavior of quantum systems.
No, not all physical observables in quantum mechanics can be represented by operators. Only observables that can be directly measured, such as position and momentum, have corresponding operators. Other physical quantities, such as time and mass, do not have corresponding operators and cannot be directly measured in a quantum mechanical system.