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

• 1 Historical background
• 1.1 Wave functions and wave equations in modern theories
• 2 Definition (one spinless particle in one dimension)
• 2.1 Position-space wave functions
• 2.1.1 Normalization condition
• 2.1.2 Quantum states as vectors
• 2.2 Momentum-space wave functions
• 2.3 Relations between position and momentum representations
• 3 Definitions (other cases)
• 3.1 One-particle states in 3d position space
• 3.2 Many-particle states in 3d position space
• 3.2.1 Probability interpretation
• 4 Time dependence
• 5 Non-relativistic 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

Reflection

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• Reflection 2 -
• Reflection 3 -

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.
But this could also be the all the electrons in an atom. This raises the same problem: How do you measure the mass, position and speed of each electron?

The wave function is a complex-valued 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 non-relativistic 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

In 1900, Max Planck postulated the proportionality between the frequency f of a photon and its energy E, E=hf, and in 1916 the corresponding relation between a photon's momentum p and wavelength lambda, lambda=hp where h is the Planck constant.

What is discussed here is the mathematical description, wavelength of a photon.
This is completely different as the wavelength of the universe.
When a photon has momentum (p=mv) this implies it also has a mass.

In 1923, De Broglie was the first to suggest that the relation lambda=h/p, now called the De Broglie relation, holds for massive particles, the chief clue being Lorentz invariance, and this can be viewed as the starting point for the modern development of quantum mechanics. The equations represent wave–particle duality for both massless and massive particles.

This raises the question if massless particles have Energy, but most of all what means massless.

In 1926, Schrödinger published the famous wave equation now named after him, the Schrödinger equation. This equation was based on classical conservation of energy using quantum operators and the de Broglie relations and the solutions of the equation are the wave functions for the quantum system. However, no one was clear on how to interpret it.

That makes it difficult to understand.