Comments about "Wave function" in Wikipedia
This document contains comments about the article Wave function in Wikipedia
 The text in italics is copied from that url
 Immediate followed by some comments
In the last paragraph I explain my own opinion.
Contents
Reflection
Introduction
The article starts with the following sentence.

A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system.

I expect that an isolated quantum system a single electron is. But how do you measure one parameter of a single a single electron? This identifies the problem of wave functions.

The wave function is a complexvalued probability amplitude, and the probabilities for the possible results of measurements made on the system can be derived from it.
That means more measurements have to be made of the same object, which is impossible, because each measurement will change the state of the object.








According to the superposition principle of quantum mechanics, wave functions can be added together and multiplied by complex numbers to form new wave functions and form a Hilbert space.

That may be true, but if it is already difficult to calculate one wave function, than what is the purpose?





In Born's statistical interpretation in nonrelativistic quantum mechanics,the squared modulus of the wave function, ?2, is a real number interpreted as the probability density of measuring a particle as being at a given place – or having a given momentum – at a given time, and possibly having definite values for discrete degrees of freedom.

The problem is that the start point to calculate the wave function is statistics i.e. observations. That makes the reasoning in this sentence difficult to understand.


1 Historical background










1.1 Wave functions and wave equations in modern theories










2 Definition (one spinless particle in one dimension)










2.1 Positionspace wave functions










2.1.1 Normalization condition










2.1.2 Quantum states as vectors










2.2 Momentumspace wave functions










2.3 Relations between position and momentum representations










3 Definitions (other cases)










3.1 Oneparticle states in 3d position space










3.2 Manyparticle states in 3d position space










3.2.1 Probability interpretation










4 Time dependence










5 Nonrelativistic examples










5.1 Finite potential barrier










5.2 Quantum harmonic oscillator










5.3 Hydrogen atom










6 Wave functions and function spaces










6.1 Vector space structure










6.2 Representations










6.3 Inner product










6.4 Hilbert space










6.5 Common Hilbert spaces










6.6 Simplified description










7 More on wave functions and abstract state space










8 Ontology










9. See also
Following is a list with "Comments in Wikipedia" about related subjects
Reflection 1  General
The wave function is a mathematical function and more specific a complex mathematical function.
See specific for the figure at the top left corner. The wave function is a mathematical description of a physical process, based on measurements. It are the dificulties of these measurements that are the major problem with the concept of the wave functions,
Reflection 2
Reflection 3
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Created: 19 January 2022
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