Why is psi^* psi dx a probability density - Griffiths

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SUMMARY

The discussion centers on the justification of the expression ψ*ψdx as a probability density for a particle located between x and x+dx, particularly in the context of quantum mechanics as outlined in Griffiths' texts. Participants highlight that while light's electric field (E-field) and diffraction by a slit are relevant, light does not conform to Schrödinger's Equation due to its massless nature. The probability density is defined as |ψ(x,t)|^2 dx, which stems from the zero probability at a point. Additionally, the relationship between energy, E^2, and intensity, which is proportional to the number of photons, is explored.

PREREQUISITES
  • Understanding of quantum mechanics principles, particularly wave functions.
  • Familiarity with Griffiths' Quantum Mechanics textbook.
  • Knowledge of electric fields and their relation to light behavior.
  • Basic concepts of probability density functions in quantum physics.
NEXT STEPS
  • Research the derivation of probability density functions in quantum mechanics.
  • Study the relationship between electric field intensity and photon count.
  • Explore the implications of massless particles in quantum mechanics.
  • Learn about the role of diffraction in quantum wave functions.
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Students preparing for quantum mechanics exams, educators seeking to clarify concepts in Griffiths' texts, and physicists interested in the foundational aspects of probability density in quantum theory.

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Justification of ψ*ψdx as probability density of particle between x and x+dx using light's E-field and diffraction by slit.

This isn't a homework problem, rather it was on the list of things to know for the exam. They don't really go over it in Griffiths Quantum Mechanics books. So are any good resources out there on this topic?
 
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I'll put what I know down as well. I know that light doesn't work with Schrödinger's Equation, because it's massless. The probability that a particle is in (x, x+dx)=|ψ(x,t)|^2 dx (comes from probability at a point being zero).

energy is proportional to E^2, from the pon. vector we know ExB~EB~E^2 & we can reason intensity is proportional to E^2 and also to the # of photons.

Where I'm really stuck is how to relate E^2 to ψ^2.
 

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