Questions about operators in QM

In summary, the person named Atif Elahi from Pakistan is seeking help with understanding operators in quantum mechanics. They have been advised to post their questions on the Physics Forums website for public discussion and peer review.
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atifelahi
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helow guys i am atif elahi from pakistan i have some problem in topic operators in quantum mechanics can you people help me
i shall be very thankful to you thanks
 
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  • #2
If you have general questions, please feel free to post them. If you have questions about homework exercises or assignments, please post them in the Homework & Coursework Questions section here on PF, probably in the Advanced Physics forum.

I see that in other threads you've tried to ask for help via e-mail. I deleted those postings because they're basically duplicates of this one. I think most people here would rather discuss questions publically, so that other people who read this forum can benefit from the discussion. Also, if the discussion is public, you get the benefit of "peer review" of the answers. Other people can post corrections if they think there are mistakes.
 
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  • #3


Hi Atif,

I am happy to assist you with your questions about operators in quantum mechanics. Operators are an essential concept in quantum mechanics as they represent physical observables, such as position, momentum, and energy. They are represented by mathematical symbols and used in equations to describe the behavior of quantum systems.

Some key properties of operators in quantum mechanics include linearity, meaning that they can be added, subtracted, and multiplied by constants, and Hermiticity, which means that they are equal to their own complex conjugate. These properties allow us to use operators to make predictions about the behavior of quantum systems.

There are also different types of operators, such as unitary operators, which preserve the norm of a wavefunction, and Hermitian operators, which have real eigenvalues. These types of operators have important implications for the behavior and measurements of quantum systems.

I hope this helps to clarify some of your questions about operators in quantum mechanics. If you have any specific questions or need further clarification, please don't hesitate to ask. Good luck with your studies!

 

Related to Questions about operators in QM

1. What are operators in quantum mechanics?

Operators in quantum mechanics are mathematical symbols that represent physical quantities, such as position, momentum, and energy. They act on wavefunctions to produce new wavefunctions, which are used to describe the behavior of quantum systems.

2. How are operators used in quantum mechanics?

Operators are used in quantum mechanics to make predictions about the behavior of quantum systems. By applying operators to wavefunctions, we can calculate the probabilities of observing certain values for physical quantities, as well as how those values may change over time.

3. What is the difference between Hermitian and non-Hermitian operators?

Hermitian operators are self-adjoint, meaning they are equal to their own adjoint (complex conjugate transpose). This allows for the eigenvalues (possible outcomes) of Hermitian operators to be real numbers, which correspond to physically observable quantities. Non-Hermitian operators, on the other hand, do not have this property and can have complex eigenvalues.

4. Can operators in quantum mechanics be visualized?

While operators themselves cannot be visualized, their effects can be visualized through the use of mathematical tools such as matrix representations and diagrams. These can help to provide a better understanding of how operators act on wavefunctions and how they relate to physical quantities.

5. How do operators in quantum mechanics relate to classical mechanics?

Operators in quantum mechanics are analogous to observables in classical mechanics. Both represent physical quantities and can be used to make predictions about a system's behavior. However, in quantum mechanics, the properties of operators are described by mathematical principles such as commutation and uncertainty relations, which do not exist in classical mechanics.

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