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Single particle Interference – Photon Vs Electron Vs Buckyball 
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#1
May1811, 05:21 AM

P: 915

Is the mechanism behind the single particle interference between photon, electron and buckyball different?
Reason for interference Photon  interference caused by maxwell electromagnetic waves? Electron  interference caused by Schroedinger probability waves? Buckyball  interference caused by Schroedinger probability waves? Pass through slits? Photon  dunno (maybe through both slits?)..breaks and combines into one, perhaps Electron  dunno....breaks and combines into one, perhaps Buckyball  must be passing through one of the slits, else it might break? 


#2
May1811, 07:14 AM

P: 661

The mechanism is the same, each of the particles is described by a probabilty wave until it is measured, the probability wave goes through both slits and is the reason for the interference pattern in all cases.
For a photon, the wave equation is described by Maxwell's equations, it is remarkable that this 19th Century model is still consistent with modern QFT model for the photon. For an electron/buckyball at slow speed a schrodinger wave eqn could accurately describe the probability wave if you could manage to solve for the boundary conditions at the slits and detection screen, for fast moving electrons maybe the Dirac eqn is needed. The easier method is a path integral calculation, Feynman shows this in his book on path integrals. If you try to wonder about which slit the particles go through or what the particles are "doing" before they are detected you will just get confused, you have to accept the probabilistic ontology between emitter and detector, whether that probabilistic ontology is described by a field theory, wave eqn or path integral is up to you. Some realist interpretations of QM like de broglie bohm try to say a particle does go through one of the slits and is guided by a pilot wave which cause the interference pattern to appear, but this is not so popular and maybe only useful as a heuristic model for understanding the resulting patterns. As the particles get bigger (like buckyballs) it gets experimentally difficult to avoid decoherence effects preventing the probability wave from producing clean interference patterns at the detection screen. 


#3
May1811, 07:23 AM

PF Gold
P: 1,376

But photons and matter particles are rather different. So I would rather say that no, physical mechanism is different. In case of matter particles Bohmian interpretation is closest description for that mechanism. But in case of photons it's ensemble interpretation (so it's not single photon interference). But then it's just my viewpoint. 


#4
May1811, 07:35 AM

P: 525

Single particle Interference – Photon Vs Electron Vs Buckyball
In Ballentine approach. He believes those destructive interference region are caused by scattering angle.. not because of intereference (he didn't believe in the wave part):
"For a crystal or diffraction grating there is only a discrete set of possible scattering angles because momentum fransfer to and from a periodic object is quantized by a multiple of delta p = h/d, where delta p is the component of momentum tranfer parallel to the direction of the periodic displacement d." Is it true? 


#5
May1811, 07:49 AM

P: 661

http://www.hitachi.com/rd/research/em/doubleslit.html 


#6
May1811, 08:06 AM

P: 525




#7
May1811, 08:23 AM

P: 661




#8
May1811, 08:46 AM

P: 3,014

The only difference is the energy  momentum relation for each particle. SInce the wavelength of the De Broglie wave determines the interference pattern (in the same experimental setup geometry), we have:
[tex] \lambda_{dB} = \frac{h}{p} [/tex] If the particles are accelerated by gaining kinetic energy [itex]K[/itex], then: [tex] (K + m c^{2})^{2} = (p c)^{2} + (m c^{2})^{2} [/tex] [tex] K^{2} + 2 m c^{2} \, K = (p c)^{2} [/tex] [tex] p = m c \, \sqrt{\frac{K}{m c^{2}} \, (2 + \frac{K}{m c^{2}})} [/tex] Finally, we have the expression: [tex] \lambda_{dB} = \frac{\lambda_{C}}{\sqrt{\frac{K}{m c^{2}} \, (2 + \frac{K}{m c^{2}})}}, \ \lambda_{C} = \frac{h}{m c} [/tex] where [itex]\lambda_{C}[/itex] is the Compton wavelength of the particle. This equation is inapplicable for massless particles. For them: [tex] E = K = p c [/tex] and: [tex] \lambda_{dB} = \frac{h c}{K} [/tex] This is the ultrarelativistic limit. In the opposite limit when the kinetic energy is much smaller than the rest energy ([itex]m c^{2}[/itex]) of the particle, we have the approximate expression: [tex] \lambda_{dB} = \frac{\lambda_{C}}{\sqrt{2 \frac{K}{m c^{2}}}} = \frac{h}{\sqrt{2 m K}} [/tex] where the speed of light does not enter anymore. This is the nonrelativistic limit. We see that in the nonrelativistic case, the de Broglie wavelength is inversly proportional to the square root of the kinetic enrgy and in the ultrarelativistic limit inversly proportional to the kinetic energy. If we plot [itex]y \equiv \lambda_{C}/\lambda_{dB}[/itex] vs. [itex]x \equiv K/(m c^{2})[/itex] on a loglog plot, we get the two asymptotic behaviors: 


#9
May1911, 11:45 AM

P: 915

are you saying that the fringes in the interference pattern would different in their thickness, spacing (between fringes) etc? 


#10
May1911, 01:00 PM

P: 3,014




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