Collapse of the wave function

This separation will allow the students to properly assess the measurement process, which plays a special and complex role in QM that is different from its role in any classical theory. Just as Kepler s laws only cover the free-falling part of the trajectories and the course corrections, essential as they may be, require tabulated data, so too in QM, it should be made clear that the Schrbdinger equation governs the dynamics of QM systems only and measurements, for now, must be treated by separate mles. Thus the problem of inaccurate boundaries of applicability can be addressed by clearly separating the two incompatible principles governing the change of the wave function the Schrbdinger equation for smooth evolution as one, and the measurement process with the collapse of the wave function as the other. 

For the usual interpretation, once the photon is detected at D2, nothing more from 2 remains in the interferometer because of the collapse of the wave-function. Therefore at detector Dj only the wave 2 from the usual source arrives. Since the path of this wave does not cross the phase shifting device and, even more, is only one wave, the coincidence count does not depend on the phase. 

If the wave function that describes the state of the system has the form given by Eq. (1.17) and does not reduce to a single term f = 4>k, then the result of the measurement of the quantity A cannot be foreseen. We will measure some eigenvalue of the operator A, but cannot predict which one. After the measurement is completed, the wave function of the system represents the eigenstate that corresponds to the measured eigenvalue (known as the collapse of the wave function). According to the postulate, the only thing to say about the measurements is that the... 

Since the early days of quantum mechanics, many scholars were trying to rationalize the paradox. always relying on some particular interpretation of quantum mechanics. In one of the interpretations, quantum mechanics does not describe a single system, but rather an infinite set of systems. We have therefore plenty of cats and the same number of boxes, each of them with the same macabre gear inside. Then, the paradox disappears, because, after the boxes are open, in 50% of cases, the cats will be alive, and in 50%, they will be dead. In another interpretation, it is criticized that Schrddinger treats the box as a quantum system, while the observer is treated classically. In this interpretation, not only Schrddinger plays the role of the observer, but also the cat, and even the box itself (since it may contain a camera). What happened may be described differently by each of the observers, depending on what information they have about the whole system. For example, in the cat (alive or dead), there is information about what has happened even before the box is open. The human observer does not have this information. Therefore, the collapse of the wave function happened earlier for the cat and later for the observer Only after the box is open, it will turn out for both the cat and the observer that the collapse happened to the same state. 

In this unique book, many questions that arise beyond the standard streamlined presentation of quantum theory are addressed. The reader finds insightful essays on the emergence of classical physics from quantum physics and the decoherence mechanism, the measurement problem and the collapse of the wave function, and many other related subjects. 

Meillassoux is well aware that quantum physics, with its uncertainty principle and the assertion of the role the observer plays in the collapse of the wave function, seems to undermine the notion of objective reality independent of any observer and thus gives an unexpected boost to Kantian transcendentalism. However, as he points out, their similarity is deceptive, obfuscating a fundamental difference Certainly, the presence of an observer may eventually affect the effectuation of a physical law, as is the case for some of the laws of quantum physics—but the very fact that an observer can influence the law is itself a property of the law which is not supposed to depend upon the existence of an observer. " In short, while, in Kant s transcendentalism, the observer -subject constitutes what he observes, in quantum physics, the observer s active role itself is reinscribed into physical reality. 

Bohr imagined that something strange happens when a photon (or electron) is detected. Before the detection, the wave function represents the probability that the photon might be detected at a particular position. After the detection, it must change to represent the new state of affairs - either the photon is there (probability 1) or not (probability 0). This means that the wave function changes everywhere whenever a measurement or observation is made. This is known as the collapse of the wave function. 

Rgure 12.7 Collapse of the wave function during the photoelectric effect... 

All the approaches can be summarized under the keyword quantum parallelism. This term was introduced by Deutsch in [4], Generally speaking, quantum parallelism is a method to compute in parallel on a serial computer. The main idea is to prepare the initial state of a quantum computer as a superposition of n states where each state corresponds to the initial state of a classical, reversible Turing machine. Then it is in principle possible to perform n computations in parallel as will be explained below. Of course, eventually a measurement has to be performed in order to read out a final result. This will lead to a collapse of the wave function, discarding most of the information about the superimposed states. The problem is how to read out a result and thereby gain more information than is available in a state that corresponds to the final state of one classical machine. We will now be more specific. 

A term that is nearly synonymous with complex numbers or functions is their phase. The rising preoccupation with the wave function phase in the last few decades is beyond doubt, to the extent that the importance of phases has of late become comparable to that of the moduli. (We use Dirac s terminology [7], which writes a wave function by a set of coefficients, the amplitudes, each expressible in terms of its absolute value, its modulus, and its phase. ) There is a related growth of literatm e on interference effects, associated with Aharonov-Bohm and Berry phases [8-14], In parallel, one has witnessed in recent years a trend to construct selectively and to manipulate wave functions. The necessary techifiques to achieve these are also anchored in the phases of the wave function components. This bend is manifest in such diverse areas as coherent or squeezed states [15,16], elecbon bansport in mesoscopic systems [17], sculpting of Rydberg-atom wavepackets [18,19], repeated and nondemolition quantum measurements [20], wavepacket collapse [21], and quantum computations [22,23], Experimentally, the determination of phases frequently utilizes measurement of Ramsey fringes [24] or similar" methods [25]. 

The interaction of the atoms in state a with the second magnet collapses the wave function a to either a or P with equal probabilities. 

The imaging process is influenced by interactions between the wave functions of the substrate and tip that result in significant deviation from the idealized square barrier profile. This is particularly true at small tip-substrate separations, where the barrier collapses below the vacuum level, as indicated in Fig. 8 for the Al-Al junction [56,64]. These calculations indicate that for typical STM imaging conditions, the top of the barrier... 

The effect of vapour pressure is most easily visualised when the rates of degradation are plotted as a function of the enthalpy of vaporisation (Fig. 5.14). Plainly the lower the enthalpy of vaporisation (Ai-f ), the more volatile the solvent and the more solvent vapour will enter the bubble. This effectively cushions the collapse of the bubble, so that the movement of solvent is slowed down, lessening the shock wave thereby leading to lower degradation rates. 

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