Expectation Value of Position for Even Wavefunction

hellsteiger
Messages
13
Reaction score
0

Homework Statement



Hello, I need to calculate the expectation value for position and momentum for a wavefunction that fulfills the following relation:

ψ0(-x)=ψ0(x)=ψ*0(x)

The wave function is normalised.


Homework Equations



There is also a second wave equation that is orthogonal to the first:

ψ1=Nd0/dx

I also need to calculate <x> and <p> for this wavefunction, also normalised.


The Attempt at a Solution



I am tempted to go ahead and say that the expectation value for position for both wavefunctions is 0, as they are both even. As for momentum I am not certain as to how i should proceed, inserting the relevant operator just seems to indicate to me momentum will be zero.
 
Physics news on Phys.org
Correction:

ψ1=Ndψ0/dx
 
I should point out that ψ1 is actually an odd function, being the derivative of an even function, it is not even as i stated earlier.
 
Just write down the expectation values of position and momentum in terms of the wave function (the position representation of the quantum state). Then discuss the mathematics given the symmetry properties, i.e., either even or odd, of the wave functions.
 

Thread 'Please tell me where I am going wrong in this integral'

##|\Psi|^2=\frac{1}{\sqrt{\pi b^2}}\exp(\frac{-(x-x_0)^2}{b^2}).## ##\braket{x}=\frac{1}{\sqrt{\pi b^2}}\int_{-\infty}^{\infty}dx\,x\exp(-\frac{(x-x_0)^2}{b^2}).## ##y=x-x_0 \quad x=y+x_0 \quad dy=dx.## The boundaries remain infinite, I believe. ##\frac{1}{\sqrt{\pi b^2}}\int_{-\infty}^{\infty}dy(y+x_0)\exp(\frac{-y^2}{b^2}).## ##\frac{2}{\sqrt{\pi b^2}}\int_0^{\infty}dy\,y\exp(\frac{-y^2}{b^2})+\frac{2x_0}{\sqrt{\pi b^2}}\int_0^{\infty}dy\,\exp(-\frac{y^2}{b^2}).## I then resolved the two...
View full post »

Thread 'Direction of the magnetic field of an oscillating charge'

Hello everyone, I’m considering a point charge q that oscillates harmonically about the origin along the z-axis, e.g. $$z_{q}(t)= A\sin(wt)$$ In a strongly simplified / quasi-instantaneous approximation I ignore retardation and take the electric field at the position ##r=(x,y,z)## simply to be the “Coulomb field at the charge’s instantaneous position”: $$E(r,t)=\frac{q}{4\pi\varepsilon_{0}}\frac{r-r_{q}(t)}{||r-r_{q}(t)||^{3}}$$ with $$r_{q}(t)=(0,0,z_{q}(t))$$ (I’m aware this isn’t...
View full post »

Thread 'Initial conditions for orbits around a wormhole'

Hi, I had an exam and I completely messed up a problem. Especially one part which was necessary for the rest of the problem. Basically, I have a wormhole metric: $$(ds)^2 = -(dt)^2 + (dr)^2 + (r^2 + b^2)( (d\theta)^2 + sin^2 \theta (d\phi)^2 )$$ Where ##b=1## with an orbit only in the equatorial plane. We also know from the question that the orbit must satisfy this relationship: $$\varepsilon = \frac{1}{2} (\frac{dr}{d\tau})^2 + V_{eff}(r)$$ Ultimately, I was tasked to find the initial...
View full post »

Similar threads

B A stupidly basic question about expectation value
Replies
8
Views
2K
What are the expectation values for position and momentum in states Ψ0 and Ψ1?
Replies
3
Views
2K
Finding meaning in the Phase of the wavefunction
Replies
11
Views
1K
Computing the wave function of a square potential
Replies
4
Views
2K
Normalisation of the radial wavefunction in 2s state?
Replies
1
Views
4K
What is the expected momentum value for a real wavefunction?
Replies
1
Views
2K
Expectation value of energy in infinite well
Replies
1
Views
4K
Possible Results and Probabilities of a Measurement of Operator Q
Replies
7
Views
2K
Expectation value in quantom mechanics (a general question)
Replies
1
Views
1K
Expected Energy Value of a Time Independent Wave
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top