Graphing Wave Function Phi(x): What Does It Look Like?

[alias25]

what would a wave function of

phi(x) = Ke^(-a|x|)

look like?

would it be like an exponential graph with a graph reflected along the y axis?

and its probability distrubution (phi)^2?
i have no idea...i can't seem to find it by googling.

 

[Max Eilerson]

would it be like an exponential graph with a graph reflected along the y axis?
.

Yes. Try plotting a few values

and its probability distrubution (phi)^2?

$$|\Psi (x)|^2$$ is the probability density.

The probability of measuring a position in the interval [a, b] is the integral of $$|\Psi (x)|^2$$ evaluted between a and b, make sure to normalise the wavefunction first.
nb: This is 1-particle in 1-dimension, which is what I suspect you want.

 

[kyle8921]

I can provide some insight into what a wave function of phi(x) = Ke^(-a|x|) might look like. This wave function is a Gaussian wave packet, which means it has a bell-shaped curve. The parameter 'a' determines the width of the curve, with smaller values of 'a' resulting in a wider curve and larger values of 'a' resulting in a narrower curve. The parameter 'K' determines the amplitude of the curve.

The graph of this wave function would indeed look like an exponential graph, but with a slight difference. The graph would be symmetric about the y-axis, with the peak at x=0 and decreasing exponentially as x moves away from 0 in both positive and negative directions. This is because of the absolute value sign in the equation.

The probability distribution of this wave function, which is given by (phi)^2, would also be a bell-shaped curve. This is because the probability of finding a particle at a particular position is proportional to the square of the wave function. The higher the amplitude of the wave function, the higher the probability of finding the particle at that position.

I hope this helps in understanding what a wave function of phi(x) = Ke^(-a|x|) would look like. It's important to note that this is just one example of a wave function and there are many other forms that wave functions can take depending on the system being studied.