In quantum mechanics, there are two interference mechanisms between identical particles. One is that the de Broglie wavelengths of two interference waves are the same, which is called the equal wavelength interference mechanism. There have been many experiments by this mechanism. The other is that the wavelengths of interference waves can also be different, in which case there should be an exchange term in addition to the direct term in the wave function. There is a fixed phase difference between the two terms, which causes interference. This is called exchange effect interference mechanism. There is a special case where two interference waves can satisfy both the two mechanisms. We propose an experiment to discriminate that in this case which mechanism plays a role on earth. By the exchange effect interference mechanism, it is possible to construct artificial crystals and to study the physical properties of this kind of crystals.
In quantum mechanics, there are two interference mechanisms between identical particles. One is that the de Broglie wavelengths of two interference waves are the same, which is called the equal wavelength interference mechanism. There have been many experiments by this mechanism. The other is that the wavelengths of interference waves can also be different, in which case there should be an exchange term in addition to the direct term in the wave function. There is a fixed phase difference between the two terms, which causes interference. This is called exchange effect interference mechanism. There is a special case where two interference waves can satisfy both the two mechanisms. We propose an experiment to discriminate that in this case which mechanism plays a role on earth. By the exchange effect interference mechanism, it is possible to construct artificial crystals and to study the physical properties of this kind of crystals.
Interference is an important observed feature in quantum mechanics. It is often seen in terms of peaks and troughs in two slit interference or in the profile of bound state wavefunction (e.g. harmonic oscillator). In this note, we argue that interference also plays a central role in determining the two types of quantum particles which exist i.e. fermions and bosons. Whereas a wavefunction is subject to a global constraint (its integral over x is 1), a local spatial probability constraint is imposed (at each x) in the case of at least two particles built from a separable wavefunction Wa(x1)Wb(x2). Here there are two indistinguishable particles, two allowable energy levels a and b and one wishes to know the probability of finding a particle at x1 and one at x2 regardless of the energy level. Let us call this P(x1,x2). The modulus squared of the wavefunction yields probability P, so a constructed wavefunction may have the property that the interchange of x1 and x2 yields a phase factor. This argument is presented often although (1) suggests it should be modified, yet the conclusion that there are only fermions and bosons remains. In this note, we consider the existence of two types of interference as the physical basis of this result. From the Schrodinger equation or from P(p/x)= a(p)exp(ipx) / W one may see that W→-W and a(p)-->-a(p) is still a solution. In quantum mechanics not only do exp(ipx) terms interfere, but eigenfunctions Wn may also interfere. Given that a bound eigenfunction may be represented by Wn or -Wn, there exists two kinds of interference. Even in the case in which there is only one particle, one may already create two possibilities: Wa(x)+Wb(x) and Wa(x)-Wb(x). If one sets a=b, the second becomes 0 at each x. This we argue already points to the idea of fermions even though only one particle is considered. This result is due strictly to alternate phase (1, -1) interference). The idea of alternate phase interference Wa-Wb also seems to be linked to a difference in wavefunction i.e. a “kind” of wavefunction representing the change in moving from energy level a to b. Thus we try to argue that there is interference beyond the usual exp(ipx) namely an alternate phase interference which applies to eigenfunctions Wn(x) and leads to the existence of fermions. Bosons occur with no alternate phase interference. These two types of particles emerge from the constraint that P(x1,x2)=P(x2,x1) i.e a local spatial probability constraint.
In a recent paper, titled “Explanation for the observed wave-particle-duality of Light” (Tank, H.K. http://vixra.org/abs/1402.0153, 2014) it was explained that: “Since at very high frequencies, narrowband filtering and generation of purely monochromatic light of one Hertz bandwidth is not yet technically possible, there has been quite a wide bandwidth of waves involved, in the double slit experiments and photoelectric experiments performed so far. And since this wide ‘band’ of waves coherently add only at discrete points in space and time, we get ‘particles’ at the detectors.” Now, to further confirm the validity of this explanation, a new kind of experiment is proposed here, in which protons and electrons are accelerated at appropriate velocities vp ve , such that their de Broglie wavelengths are equal; i.e. ( h / mp vp )= ( h / me ve ) and let them pass through closely spaced slits so that they can interfere with each other. Similarly, in another experiment, their wave-functions: A exp i ( kp X - ωp t ) = A exp i ( ke X - ωe t ) , and let them pass through closely spaced slits, and see how the two matter-waves interfere.
Abstract Chapter 11 introduces the essential mystery of quantum mechanics, shows how it is resolved, and then goes on to examine related phenomena. The mystery is how individual photons, not electromagnetic waves, can give rise to the interference pattern seen in the two-slit experiment. They are shown to do so because the relevant quantum amplitude is a linear combination of two terms, leading to the pattern when neither slit is identified as the one the photon went through, but collapsing to one term and no pattern if the slit is identified. Similar results are shown to occur when individual electrons are incident on the two slits, and when large molecules, which have de Broglie wavelengths, are scattered by diffraction gratings. Many other interference experiments are described, including those where a photon was shown to be in two places simultaneously and one where a photon displayed both wave and particle features.
We present a general theory to describe two-photon interference, including a formal description of few photon intereference in terms of single-photon amplitudes. With this formalism, it is possible to describe both frequency entangled and separable two-photon interference in terms of single-photon wave functions. Using this description, we address issues related to the physical interpretation of two-photon interference experiments. We include a discussion on how few-photon interference can be interpreted as a bosonic exchange effect, and how this relates to traditional exchange effects with fermions.
Arguments about particles or waves gave way to a recognized need for both particles and waves in the description of radiation. The confusion over particle versus wave properties was resolved by Louis de Broglie. He postulated that since light has a dual wave–particle nature, matter also has this nature. The idea was to perform a diffraction experiment with electrons. An interference pattern was demonstrated not only with electrons, but also with many kinds of material particles like protons and neutrons. However, any attempt to observe an interference pattern with neutral atoms was found difficult by the fact that atoms carried no charge as electrons do and could not penetrate through condensate matter like neutrons. The de Broglie wavelength of an electron in the smallest orbit turns out to be exactly equal to the circumference of the orbit predicted by Bohr. The interpretation of the interference phenomenon becomes more subtle when the light beams are replaced by individual photons or particles.
IT is well known from experiment, as well as from classical theory, that strictly monochromatic light waves originating from different sources do interfere.' An example in which the waves are nearly monochromatic is found in the case of radio waves, and it is known that radio waves from two stations that have the same frequency show an interference effect. We may describe the phenomenon quantum mechanically if we represent the light quanta emitted by both sources by waves in Schroedinger configuration space. So long as we consider the quanta emitted by one source as different from those emitted by the other, the total wave function will be the product of the wave functions corresponding to the quanta emanating from both sources, and there will be no interference effect. In the present paper, we will see how things are changed when we symmetrize or antisymmetrize the wave function, i.e. assume either Bose or Fermi statistics for the particles. In the simple quantum mechanical picture that we will use here, we will assume a definite number of photons coming out from each source, and this implies that the phase relations will be undetermined.2 As a result, even the symmetrized wave functions must be expected to give, at any point in space, the same density of quanta that classical theory determines, when the intensity is averaged over the phase differences between the two sources. This implies that no interference is observed between the waves from the two sources. If we want to look for an interference effect when dealing with a quantum picture in which we have a definite number of photons, we must look for a phenomenon whose classical description should be independent of the phase. We shall make use of the fact that, in classical theory,