Ok let's look at the wave number kx=nπ/L for the typical wave in 1D and this 2D solution. But we could also produce a standing wave, bound at nodes, at 45deg located in the middle of the side L equal to n45π/√L/22+L/22 - where n45is a not a whole number increment from n. This solution requires...
Hi,
I am wondering about additional solutions to the particle in a box problem. In the one dimension the wave functions allowed all make sense with nodes pinned to an infinite potential barrier at either end and then divided into node increments related to the length of the box. However, in 2...
I have seen the principle of least action also being described as stationary action. I can see that the calculus is searching for a stationary point which could be a minimum, maximum, or saddle. However, given any two fixed points there are always infinite paths between them; hence no...
Good point on the word doc - I have attached a more usable PDF file...(note the text in the word file was the same as the post so loss if it can't be read - I typed it in word first).
I have read up on both Fraunhofer and Fresnel diffraction and both appear to be fundamentally calculated in the...
Why are the orientations of waves arriving at the screen not considered when adding amplitudes?
For example a double slit in 2D has two radial lengths of R1 and R2, one from each source Slit 1 and Slit 2, arriving at point P1. (See attached) The provides a probability amplitude of...
Given the enormous response to this one I thought I might add a few more details. :smile:
Typical Amplitude Calculation
|Ψ|2=(ei(kR1-ωt)+ei(kR1-ωt))(ei(kR1-ωt)+ei(kR1-ωt))
Amplitude Calculation for adjusted orientation...
The configuration and dimensions of any experiment are important in determining wave amplitudes. Then why are the orientations of complex waves not considered when they are added?
For example in two dimensions;
To find a resulting wave at a point P1 from two paths R1 & R2 we have...
Thanks mfb.
Can you expand your answers a little more so I can look them up - or perhaps you have a good reference? I am guessing that your inferring the wave is in a configuration space like a de broglie wave? (So no 'real' relationship with the speeds of particles - it becomes a calculation...
No I think we are getting sidetracked - I don't think I am going wrong with coherence. The simple fact that we get interference at all demonstrates that there are two (or more) different path lengths for the wave function. My confusion is about time - if the probability wave function path...
It may not travel a set path - hence the interference. But we can accurately measure the velocity of a photon - so that is a distance between two points (whatever path it takes in between). As the velocity is fixed, each path has different time...would the velocity equal the time to travel the...
Yes-So wouldn't the interference be in violation of the photon's fixed velocity? If it was interference from the same crest it would make some sense but to get the interference one path is longer than the other (with maximised probabilities at x+nλ).
And still - what time would be measured -...
So this is basic question but the more I read the more I am confusing myself!
I was assuming that the wavelength of a photon was the same wavelength as the associated probability amplitude (although a complex number). So to make constructive interference it means one path takes say ten...
Yes - I agree but...
In the slot images of my first post the slit is either short or the width of the laser beam is visible - we can tell this from the fuzzy fringes in the y-axis. Note there is no interference indicated above and below the slit - but there should be given the width of the...