OutlineImagine a particle of mass m, constrained to move along the x-axis, subject to some specified force F(x,t): How does it do by CM or NM?The position of the particle at any given time x(t) can be determined by Classical Mechanics.Then, the velocity [ v(t) = dx(t)/dt ], the momentum [ p(t)=mv(t) ], the kinetic energy ( T=mv2/2 ), or any other dynamical variable of interest can be figured out ! Classical Mechanics (or Newton’s mechanics):However, Quantum Mechanics approaches this same problem quite differently! Quantum Mechanics:In this case what we are looking for is the wave function, (x,t), of the particle, and we get it by solving the Schrödinger Equation:where i is the square root of 1, and ħ is Planck’s constant:NOTE: The Schrödinger Equation, not derived but guessed at intuitively (直觉) , would then be a postulate (假设) of new theory, and its validity would have to be checked by experiment !The Schrödinger Equation plays a role logically analogous to Newton’s second law: Given suitable initial conditions [ typically, (x,t = 0) ], the Schrödinger equation determines (x,t) for all future time, just as, in classical mechanics, Newton’s law determines x(t) for all future time.Fundamental principles of Quantum Mechanics：Assumption 1: Wave function (r, t) describes the state of a particle ! Assumption 2: Schrödinger Equation What exactly is this “wave function” ? or what does it do for you once you are got it ? or how can such “wave function” be said to describe the state of a particle ? Now, Question is:The wave function (r,t) itself is complex, not any physical means, but |(r,t)|2=* ( where * is the complex conjugate of ) is real and nonnegative — as a probability, of course, must be.The answer is provided by Born’s statistical interpretation of the wave function, which says that |(x,t)|2 gives the probability of finding the particle at point x, at time t — or more precisely :For example:One would be quite likely to find that the particle in the vicinity of point A, and relatively unlikely to find it near point B. Quantum Mechanics has to offer is statistical information about the possible results ! The statistical interpretation (诠释) introduces a kind of indeterminacy (不确定性) into quantum mechanics.Even if you know everything the theory has to tell you about the particle, you cannot predict with certainty (必然的事) the outcome (结果) of a simple experiment to measure its position.This indeterminacy has been profoundly(深深地) disturbing to physicists and philosophers alike. Is it peculiarity (独特性) of nature, a deficiency (缺陷) in the theory, a fault in the measuring apparatus (仪器), or what ?Suppose we do measure the position of the particle, and we find it to be at the point C. “Measurement” of Microscopic Particle (or System)Question: Where was the particle just before we made the measurement ? Answer 1. The realist (现实的) position: The particle was at C. This certainly seems like a sensible response, and it is the one Einstein advocated. However, that if this is true then quantum mechanics is an incomplete theory, since the particle really was at C, and yet quantum mechanics was unable to tell us so. Answer 2. The orthodox(公认的) position: The particle was not really anywhere. It was the act of measurement that forced the particle to “take a stand” (表态 ) . This view is associated with Bohr and his followers --- Copenhagen interpretation.However, that if it is correct there is something very peculiar (古怪) about the act of measurement — something that over half a century of debate ( 辩论) has done precious (珍贵的) little to illuminate (阐明).Answer 3. The agnostic (不可知论的) position: Refuse to answer. This is not quite as silly as it sounds --- after all, what sense can there be in making assertions (断言) about the status of a particle before a measurement, when the only way of knowing whether you were right is precisely to conduct (实施) a measurement, in which case what you get is no longer “before the measurement”? 在一个测量前就断言一个粒子状态有什么意义？It is metaphysics (形而上学) to worry about something that cannot, by its nature, be tested.For decades this was the “fall back” position of most physicists: They’d try to sell you answer 2, but if you were persistent they’d switch to 3 and terminate (结束) the conversation.Until fairly recently, all three position (realist, orthodox, and agnostic) had their partisans (死党). Bell’s discovery effectively eliminated agnosticism as a viable (可行的) option (选择), and made it an experimental question whether 1 or 2 is the correct choice. But in 1964 John Bell astonished (使惊讶) the physics community by showing that it makes an observable (观察得到的) difference if the particle had a precise (though unknown) position prior (先前) to the measurement.For now, suffice(满足…的需要) it to say that the experiments have confirmed decisively(决然地) the orthodox inter- pretation: A particle simply does not have a precise posit。