Expectation of position in a 2D system

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Homework Help Overview

The discussion revolves around calculating the expectation of the position operator in a two-dimensional infinite potential well, specifically in the xy plane. Participants are exploring the mathematical formulation and conceptual understanding of the expectation value in quantum mechanics.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster inquires about the calculation of the expectation value of the position operator and whether the wave function is used in conjunction with the Hamiltonian. Another participant provides a mathematical expression for the expectation value, prompting further questions about the derivation and meaning of the double integral involved.

Discussion Status

The discussion is ongoing, with participants seeking clarification on the mathematical expression provided and its derivation. There is an active exchange of ideas, with some participants questioning the source of the double integral and others referencing textbook definitions related to expectation values.

Contextual Notes

Participants are navigating the specifics of quantum mechanics and the implications of using wave functions in calculations, indicating a potential need for additional context or definitions from their textbooks.

staraptor
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How does on calculate the expectation of the position operator x in a 2D infinite potential well (in the xy plane)? Do we only work with the Psi to the Hamiltonian in that particular coordinate when finding <Psi|x|Psi>?
 
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You calculate
$$\langle x \rangle = \iint \psi^*(x,y)\,x\,\psi(x,y)\,dx\,dy$$
 
Could you explain this please? Where does the double intergral come from?
 
What does your textbook say about calculating an expectation value?
 

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