– it does not involve making several values of the same physical quantity coexist within a single system.

18 We have ⟨ak|an⟩ = δkn, where δkn, called the Kronecker delta, takes the value 1 when n = k and 0 otherwise.

19 It is generally chosen to consider a vector of unit squared norm: |⟨Ψ(t)|Ψ(t)⟩|2 = 1.

20 Considering a continuous physical quantity implies defining not the probability 𝓟(x) of a value – which is mathematically zero – but an infinitesimal probability d𝓟(x) over an infinitesimal interval of length dx.

21 The same procedure applies, but even more formally, since it now involves determining the entire function Ψ(x, t) in the expression (3).

22 It is sometimes incorrectly referred to as Heisenberg’s uncertainty relations, a term that carries too much connotation because it suggests a misunderstanding of the physical state of the system, representing a very partial epistemic stance – see further below.

23 A measurement of x consists of determining the value of the position x with a precision δx, generally smaller than the spectral width ∆x.

24 In French : « Tais-toi et calcule ».

25 N.D. Mermin, «What’s Wrong with this Pillow?» Physics Today, 42, 9 (1989).

26 It is important to note that, in practice, most physicists commonly associate the state vector, the wave function, or the Hamiltonian with a given system, rather than with an ensemble of systems. This reflects a certain resistance to adopting a strictly operationalist perspective.

27 To be more concise than the expression ‘a statistical ensemble of systems’.

28 In practice, the vector obtained after state vector reduction is manually normalized to unity, in order to continue with a properly normalized vector.

29 Difficulty, or not, depending on the perspective one adopts on the entire issue.

30 For example, let’s consider the measurement of the temperature of a fluid: this measure-ment will not significantly affect the state of the system – in this case, the fluid – and, in return, the result of the measurement, as long as the heat capacity of the measured system is much greater than that of the measuring device – in this case, a thermometer

31 This situation is sometimes justified by invoking the fact that, due to the microscopic nature of the quantum system, the interaction between the measuring device and the measured system inevitably results in an exchange of action between the two systems, at least equal to ℏ, which causes a disturbance in the studied system. In reality, things are not so simple. Indeed, if we consider a system in an eigenstate of a certain operator, say Â, and we perform a measurement of the corresponding physical quantity A, this measurement will reveal with probability 1 the eigenvalue associated with the eigenstate. Therefore, we cannot consider that, in this case, the measurement actually disturbs the system. Or, we must admit that the state vector describing the system in an eigenstate of a given quantity accounts for the disturbance induced by the measurement.

32 An action corresponds to any quantity dimensioned as a kinetic moment; it is notably the product of momentum by length, or of energy by time.

33 See note 26.

34 The reader might object that, in certain circumstances – notably the most emblematic one in quantum mechanics, namely the double-slit experiment – the notion of super-position of states is not only relevant but even essential to describe a single system. Let us consider this experiment, in which photons are sent one by one toward a screen pierced with two slits. The result of this experiment is then analyzed, which is the impacts of these photons on a second screen, equipped with detectors, placed behind the first one. During this experiment, each individual impact appears to occur randomly. However, when examining the statistical distribution obtained after a large number of impacts, an interference pattern emerges. It then seems natural to conclude, based on these observa-tions, that each photon possesses a form of ubiquity or, in other words, that it is intrin-sically «carrier» of the interference phenomenon. The state that describes it before the impact on the second screen should therefore correspond to a superposition of the type |Ψ⟩ = a|T1⟩ + b|T2⟩, where |T1⟩ and |T2⟩ correspond to states associated with passing through slit 1 and slit 2, respectively. This conclusion, although intuitive, is not inevita-ble. Indeed, one could envisage a mechanism that forces each photon to pass through a specific slit, while still ensuring the appearance of an interference pattern from a large