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According to the postulates of quantum mechanics, how are observables related to operators?
- a)Every observable is associated with a Hermitian operator.
- b)Observables are inversely proportional to linear Hermitian operators.
- c)All observables are fundamentally unrelated to operators.
- d)Observables are directly proportional to non-linear Hermitian operators.
Correct answer is option 'A'. Can you explain this answer?
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According to the postulates of quantum mechanics, how are observables ...
Observable and Operator Relationship in Quantum Mechanics
Observable Associated with Hermitian Operator:
- According to quantum mechanics, observables such as position, momentum, energy, etc., are represented by operators.
- Every observable in quantum mechanics is associated with a corresponding Hermitian operator.
- Hermitian operators have special properties that ensure the observables are real and have well-defined eigenvalues.
Properties of Hermitian Operators:
- Hermitian operators have real eigenvalues, which correspond to the possible outcomes of measurements of observables.
- The eigenvectors of Hermitian operators form a complete set, allowing for the expansion of any state in terms of these eigenvectors.
- Hermitian operators play a crucial role in determining the probabilistic outcomes of measurements in quantum systems.
Significance of Hermitian Operators:
- The association of observables with Hermitian operators is a foundational concept in quantum mechanics that allows for the prediction and understanding of quantum phenomena.
- The properties of Hermitian operators ensure that observables in quantum systems behave in a consistent and predictable manner.
Therefore, the relationship between observables and operators in quantum mechanics is that each observable is associated with a Hermitian operator, highlighting the deep connection between measurements and mathematical operators in the quantum realm.
Observable Associated with Hermitian Operator:
- According to quantum mechanics, observables such as position, momentum, energy, etc., are represented by operators.
- Every observable in quantum mechanics is associated with a corresponding Hermitian operator.
- Hermitian operators have special properties that ensure the observables are real and have well-defined eigenvalues.
Properties of Hermitian Operators:
- Hermitian operators have real eigenvalues, which correspond to the possible outcomes of measurements of observables.
- The eigenvectors of Hermitian operators form a complete set, allowing for the expansion of any state in terms of these eigenvectors.
- Hermitian operators play a crucial role in determining the probabilistic outcomes of measurements in quantum systems.
Significance of Hermitian Operators:
- The association of observables with Hermitian operators is a foundational concept in quantum mechanics that allows for the prediction and understanding of quantum phenomena.
- The properties of Hermitian operators ensure that observables in quantum systems behave in a consistent and predictable manner.
Therefore, the relationship between observables and operators in quantum mechanics is that each observable is associated with a Hermitian operator, highlighting the deep connection between measurements and mathematical operators in the quantum realm.
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According to the postulates of quantum mechanics, how are observables ...
- In quantum mechanics, the measurable quantities (observables) like position, momentum, etc., are associated with corresponding operators.
- The reason for associating Hermitian operators with observables lies in their mathematical properties.
- The eigenvalues of a Hermitian operator are always real, which is a requirement for all measurements in physics (as we cannot measure complex values in an experiment).
- Therefore, to every observable in classical mechanics, we can assign a corresponding Hermitian operator in quantum mechanics.
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According to the postulates of quantum mechanics, how are observables related to operators?a)Every observable is associated with a Hermitian operator.b)Observables are inversely proportional to linear Hermitian operators.c)All observables are fundamentally unrelated to operators.d)Observables are directly proportional to non-linear Hermitian operators.Correct answer is option 'A'. Can you explain this answer?
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According to the postulates of quantum mechanics, how are observables related to operators?a)Every observable is associated with a Hermitian operator.b)Observables are inversely proportional to linear Hermitian operators.c)All observables are fundamentally unrelated to operators.d)Observables are directly proportional to non-linear Hermitian operators.Correct answer is option 'A'. Can you explain this answer? for UGC NET 2024 is part of UGC NET preparation. The Question and answers have been prepared according to the UGC NET exam syllabus. Information about According to the postulates of quantum mechanics, how are observables related to operators?a)Every observable is associated with a Hermitian operator.b)Observables are inversely proportional to linear Hermitian operators.c)All observables are fundamentally unrelated to operators.d)Observables are directly proportional to non-linear Hermitian operators.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for UGC NET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for According to the postulates of quantum mechanics, how are observables related to operators?a)Every observable is associated with a Hermitian operator.b)Observables are inversely proportional to linear Hermitian operators.c)All observables are fundamentally unrelated to operators.d)Observables are directly proportional to non-linear Hermitian operators.Correct answer is option 'A'. Can you explain this answer?.
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