• petera88
In summary, An undergrad student is having trouble understanding quantum mechanics and has joined a forum to ask for conceptual help. They are specifically struggling with the concept of the wave function and the difference between the complex conjugate psi* and just psi. They are trying to find the probability current for a free particle and are unsure how to split the time-dependent wave function into psi and psi*. They have also accidentally posted their question in the wrong section and have moved it to the appropriate homework section.
petera88
Hello. This is my first post here. I am an undergrad student and my first experience with quantum mechanics isn't going as well as I hoped. I decided I should join this form and ask question for conceptual help.

So here is my first question.

The formula for probability current has a psi(derivative psi*) - psi*(derivative psi).

I am trying to find it for a free particle. I know the time-dependent wave function for a free particle, and am assuming I just take the derivative and plug everything in. I think where I lack is my fundamental understanding of the wave function. So my question is...

What is the difference between the complex conjugate psi*, and just psi? To my understanding it is to take anything complex and make it real. I haven't done much work in my lower division math courses with complex numbers so don't understand if I am just given a time-dependent wave function, how to I split this to psi and psi*?

I moved this to the homework section. Did not realize I was posting it here. Sorry about that.

Probability current for free particles is a measure of the flow of probability density in quantum mechanics. It describes the rate at which the probability of finding a particle in a certain location changes over time.

## How is probability current calculated?

The probability current for free particles is calculated using the Schrödinger equation and the probability density function. It involves taking the complex conjugate of the wavefunction and multiplying it by the gradient of the wavefunction.

## What is the significance of probability current in quantum mechanics?

The concept of probability current is important in quantum mechanics because it allows us to understand and predict the behavior of particles at the microscopic level. It helps us to understand the probability of a particle being in a certain location at a certain time.

## Can probability current be negative?

Yes, probability current can be negative. This means that the probability density is decreasing in a particular direction, indicating that particles are moving away from that location.

## How does probability current relate to the uncertainty principle?

The uncertainty principle states that it is impossible to know both the position and momentum of a particle with absolute certainty. The concept of probability current is related to this principle as it describes the flow of probability density, which is directly linked to the uncertainty of a particle's position and momentum.

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