How Do You Calculate the Position of a Neutron Using Wave Functions?

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SUMMARY

This discussion focuses on calculating the position of a neutron using wave functions and matrix multiplication. The user inquires about the proper placement of variables within integrals and the multiplication of matrices in quantum mechanics. Key points include the clarification that the first vector under the integral should be a row vector, and that the product of the wave function and its conjugate results in a scalar value. The discussion emphasizes the importance of understanding matrix dimensions in quantum calculations.

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  • Understanding of quantum mechanics concepts, specifically wave functions.
  • Familiarity with matrix multiplication rules in linear algebra.
  • Knowledge of integrals and their properties in physics.
  • Basic grasp of scalar and vector quantities in mathematical physics.
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  • Study the principles of quantum mechanics, focusing on wave function behavior.
  • Learn about matrix operations, specifically in the context of quantum states.
  • Research the implications of scalar products in quantum mechanics.
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Students and professionals in physics, particularly those specializing in quantum mechanics, as well as mathematicians interested in the application of linear algebra in physical theories.

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Hello
I need to calculate <x> (x is the location of neutron) and the state is
untitled21.JPG

and the integral is:
untitled.JPG

Can I move the x to be near the integral symbol? and how to I multiply the matrices?

And is this true:
untitled212.JPG

Can I move the psi to be near the psi*? And psi*x psi =psi^2=1 right?

thanks
 
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The first vector under the integration should be a row, not a column as you've drawn it. [itex]\bar{x}[/itex] is a square matrix, so the full product is a scalar.
 
Last edited:

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