• The text in italics is copied from that url
• Immediate followed by some comments
In the last paragraph I explain my own opinion.

### Introduction

The article starts with the following sentence.
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles.
Okay. The emphasis is on the wordings: a physical description.
The modern theory is formulated in various specially developed mathematical formalisms.
Okay
In one of them, a mathematical entity called the wave function provides information, in the form of probability amplitudes, about what measurements of a particle's energy, momentum, and other physical properties may yield.
The problem is how this probability amplitude is measured. When a probability is considered its value has to be measured multiple times.

### 2 Mathematical formulations

In the formalism of quantum mechanics, the state of a system at a given time is described by a complex wave function, also referred to as state vector in a complex vector space.
Tricky sentence.
This abstract mathematical object allows for the calculation of probabilities of outcomes of concrete experiments.
I expect that to define a complex wave function for concrete experiments is very difficult. What is also difficult is to predict the (correct) outcome of the experiment in advance.
IMO this is only possible for certain very simple experiments.
For example, it allows one to compute the probability of finding an electron in a particular region around the nucleus at a particular time.
And how is that experimentally tested?
Contrary to classical mechanics, one can never make simultaneous predictions of conjugate variables, such as position and momentum, to arbitrary precision.
The issue is much more that one cannot experimentally test velocity at any arbitrary precision.
IMO this is an issue for all sorts of experiments.

### 4 Interactions with other scientific theories

The rules of quantum mechanics are fundamental.
I think it is better to call them: mathematical strict. (Assuming they are)
They assert that the state space of a system is a Hilbert space (crucially, that the space has an inner product) and that observables of that system are Hermitian operators acting on vectors in that space—although they do not tell us which Hilbert space or which operators.
This may be all mathematical correct. The issue is to what extend you can demonstrate each assertion based on actual experiments (observables)
An important guide for making these choices is the correspondence principle, which states that the predictions of quantum mechanics reduce to those of classical mechanics when a system moves to higher energies or, equivalently, larger quantum numbers, i.e. whereas a single particle exhibits a degree of randomness,
This raises immediate the question which types of events (processes) are described by classical mechanics and which are by quantum mechanics.
My impression is that it becomes quantum mechanics when you study at elementary particle level.

### 4.1 Quantum mechanics and classical physics

Predictions of quantum mechanics have been verified experimentally to an extremely high degree of accuracy.
I expect here at particle level. It is better to add: Certain predictions etc.
The laws of classical mechanics thus follow from the laws of quantum mechanics as a statistical average at the limit of large systems or large quantum numbers.
If you want to understand this sentence you must know what the laws of classical mechanics are and what the laws of quantum mechanics are. You need a list

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Created: 12 December 2017

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