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

In summary, the conversation discussed the justification of ψ*ψdx as the probability density of a particle between x and x+dx using light's E-field and diffraction by a slit. It was mentioned that this topic is not covered in Griffiths Quantum Mechanics books and the person was looking for additional resources. They also noted that light does not work with Schrodinger's Equation due to its masslessness. It was mentioned that energy is proportional to E^2 based on the Poynting vector, and intensity is also proportional to E^2 and the number of photons. The conversation ended with the person expressing difficulty in understanding the relationship between E^2 and ψ^2.
  • #1
kuahji
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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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  • #2


I'll put what I know down as well. I know that light doesn't work with Schrodinger'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.
 

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

What is psi^* psi dx in the context of probability density?

Psi^* psi dx is a mathematical expression used in quantum mechanics to represent the probability density of a quantum system. It is derived from the wave function, psi, which describes the state of a particle in terms of its position and time. Psi^* is the complex conjugate of psi, and when multiplied by psi and integrated over all space (dx), it gives the probability of finding the particle at a specific position.

Why is psi^* psi dx considered a probability density?

In quantum mechanics, the probability of finding a particle in a particular location is not a definite value, but instead is described by a probability distribution. Psi^* psi dx represents this probability distribution, as it gives the probability of finding the particle at a specific position within a given volume of space (dx). Therefore, it is considered a probability density.

How is psi^* psi dx related to the uncertainty principle?

The uncertainty principle states that it is impossible to simultaneously know the exact position and momentum of a particle. Psi^* psi dx is related to this principle in that it represents the probability of finding a particle at a particular position, but it does not provide information about its momentum. This uncertainty in position and momentum is inherent in the probabilistic nature of quantum mechanics.

Can psi^* psi dx be used to calculate the probability of finding a particle in a specific region?

Yes, psi^* psi dx can be used to calculate the probability of finding a particle in a specific region. By integrating the expression over a certain volume of space (dx), the resulting value gives the probability of finding the particle within that volume. This allows for the calculation of probabilities for different regions and can be used to predict the behavior of quantum systems.

What is the significance of psi^* psi dx in quantum mechanics?

Psi^* psi dx is a fundamental concept in quantum mechanics, as it represents the probabilistic nature of quantum systems. It allows for the calculation of probabilities for different positions and provides insight into the behavior of particles at the quantum level. Without this concept, it would be impossible to accurately describe and predict the behavior of particles in quantum systems.

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