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狄拉克《量子力学原理》书摘（1－10节）
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Causality
"Causality applies only to a system which is left undisturbed. If a system is small, we cannot observe it without producing a serious disturbance and hence we cannot expect to find any causal connextion between the results of our observations."
Wave and particles
"The essential point is the association of each of the translational states of a photon with one of the wave functions of ordinary wave optics. The nature of this association cannot be pictured on a basis of classical mechanics, but is something entirely new. It would be quite wrong to picture the photon and its associated wave as interacting in the way in which particles and waves can interact in classical mechanics. The association can be interpreted only statistically, the wave function giving us information about the probability of our finding the photon in any particular place when we make an observation of where it is."
Physical pictures
"……the main object of physical science is not the provision of picutres, but is the formulation of laws governing phenomena and the application of these laws to the discovery of new phenomena. If a picture exists, so much the better; but whether a picture exists or not is a matter of only secondary importance."
Superposition of states (简单说就是态叠加只是改变每个结果被测得的概率，结果本身不会变化。)
"The intermediate character of the state formed by superposition thus expresses itself through the probability of a particular result for an observation being intermediate between the corresponding probabilities for the original states, not through the result itself being intermediate between the corresponding results for the original states."
"State of rest"
"Again, while there exists a classical state with zero amplitude of oscillation everywhere, namely the state of rest, there does not exist any corresponding state for a quantum system, the zero ket vector corresponding to no state at all."
Properties of real operator
"……, it should be noted that, if xi and eta are real, in general xieta is not real. This is an important difference from classical mechanics. However, xieta+etaxi is real, and so is i(xieta-etaxi). Only when xi and eta commute is xieta itself also real."
Dynamical Variable
"When we make an observation we measure some dynamical variables. It is obvious physically that the result of such a measurement must always be a real number, so we should expect that any dynamical variable that we can measure must be a real dynamical variable. One might think one could measure a complex dynamical variable by measuring separately its real and pure imaginary parts. But this would involve two measurements or two observations, which would be all right in classical mechanics, but would not do in quantum mechanics, where two observations in general interfere with one another--it is not in general permissible to consider that two observations can be made exactly simultaneously, and if they are made in quick succession the first will usually disturb the state of the system and introduce an indeterminacy that will affect the second."
Complete Set
"Now these states into which the system may jump are all eigenstates of xi, and hence the original state is dependent on eigenstates of xi. But the original state may be any state, so we can conclude that any state is dependent on eigenstates of xi. If we define a complete set of states to be a set such that any state is dependent on them, then our conclusion can be formulated-the eigenstates of xi form a complete set."
Observable
"Not every real dynamical variable has sufficient eigenstates to form a complete set. Those whose eigenstates do not form complete sets are not quantities that can be measured. We obtain in this way a further condition that a dynamical variable has to satisfy in order that it shall be susceptible to measurement, in addition to the condition that it shall be real. We call a real dynamical variable whose eigenstates form a complete set an observable. Thus any quantitiy that can be measured is an observable."
Hilbert space
"The space of bra and ket vectors when the vectors are restricted to be of finite length and to have finite scalar products is called by mathematicians Hilbert space."
https://m.sciencenet.cn/blog-117333-340074.html
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