# Physical meaning of wavefunction parameters x and t

• accountkiller
In summary, the parameters of a wave function describe its position and amplitude at a particular time.
accountkiller
This isn't a homework question per se but it's a question that I had while reading through my textbook so I think it's appropriate here. I just started studying Quantum Mechanics and so am getting familiarized with the meaning of wave functions and their behavior. One question I can't seem to find the answer to no matter what keywords I use in Google is the following:

What do the parameters of ψ(x,t) mean? When I imagine a 2D wave on a graph, I see a wave periodically going up and down along the x-axis, so parameter x (position). But the y-axis is not time, it's the amplitude. So where does the parameter 't' fit into this graph?

It feels like it should be a simple thing I should know but I do not and cannot find a good resource, so if anyone could help me understand its meaning, I'd appreciate it. Thanks1

Oh and similarly, another thing I don't quite understand and that I can't find on the internet is:

Where does the (kx-ωt) term come from in the wave function equation ψ(x,t) = ∫ A(k) e^i(kx-ωt) dk ? Essentially, I'm looking for a derivation of the wave function (typing that into Google somehow does not give me the right results).

So where does the parameter 't' fit into this graph?

Imagine the graph is animated so the wave moves from left to right (or from right to left). Then to see what the graph looks like at a particular time, substitute the appropriate value of t. Different values of t give you "snapshots" of the wave (ψ versus x) at different times.

jtbell: Ahh, thank you for that clear image! That's what I was looking for.

Sonderval: That is a pretty great blog you have there - I love that it's full of animations. I haven't gotten a chance to sit down and read it but I did skim over it and have added it to my Bookmarks to review when I get a free moment. Cool work!

Thank you both for the help :)

## 1. What is the physical meaning of the wavefunction parameters x and t?

The wavefunction parameters x and t represent the position and time of a particle in a quantum system. The wavefunction itself is a mathematical representation of the probability amplitude of finding the particle at a particular position and time.

## 2. How are the wavefunction parameters x and t related?

The wavefunction parameters x and t are closely related through the Schrodinger equation, which describes how the wavefunction changes over time. The position x and time t are independent variables in the equation.

## 3. Can the wavefunction parameters x and t be measured directly?

No, the wavefunction parameters x and t cannot be measured directly. The wavefunction itself is a mathematical concept and cannot be directly observed. However, the probability of finding a particle at a certain position and time can be measured through experiments.

## 4. How do the wavefunction parameters x and t affect the behavior of a particle?

The wavefunction parameters x and t determine the probability of finding a particle at a specific position and time. As the particle moves through space and time, its wavefunction will change accordingly, affecting the likelihood of finding it in different locations at different times.

## 5. Are the wavefunction parameters x and t constant?

No, the wavefunction parameters x and t are not constant. They change over time as the particle's wavefunction evolves according to the Schrodinger equation. The values of x and t at any given moment are determined by the initial conditions of the system and the potential energy function.

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