In Quantum mechanics a microscopic / quantum particle is described by the wave packet. The mathematical function, which describes or represents the wave packet is known as wave function. A wave packet is the linear combination or superposition of all the harmonic waves confined in the small region of space around the quantum (microscopic) particle.

Wave function is a probability in amplitude in Quantum mechanics describing the quantum state of the particle and how it behaves.Typically It is function of position and time. Wave function does not have physical meaning but square of the wave function |ψ|2 gives the probability density of particle in a place at a given time.

Thank you very much

My question about if something has not physical meaning, can i get a physical meaning from it? in other words, can i get from nonexistence thing an existing thing.

@ Mukhlis Ismail : Just consider wave function as some mathematical quantity alone.. Physical meaning comes only when it comes with its conjugate . ie: psi with psi-star ..

The difficulties of explicating the 'physical meaning' in quantum mechanics has been discussed from the beginning of quantum physics. Here are some references for researching the issue.

1) Discussion with Einstein on Epistemological Problems in Atomic Physics (1949), Niels Bohr, Atomic Physics and Human Knowledge. Dover Press.

2) Quantum Theory, David Bohm, (1951, 1979), Chapter 8, An Attempt to Build a Physical Picture of the Quantum Nature of Matter.

3) The Story of Quantum Mechanics, Victor Guillemin, (1968), Chapter 6, Matter Waves. Charles Scribner's Sons.

4) Conversations on the Dark Secrets of Physics, Edward Teller, (1991), Chapter 9. The Correspondence Principle. Perseus Publishing.

5) The Principles of Quantum Mechanics, Paul Dirac, (1958), Oxford University Press.

What is meant by ' wave function has no physical meaning' is that it is not something that can be measured. The 'values' of wavfunction are (in general) complex numbers and therefore they do not represent measurable physical quantities.

Saying wavefunction has "no meaning" is not a good way to put it, and I think you do not find such statements in good text books. It obviously has a great deal of physical meaning - that is why we take so much pains to find it!

Don

I think that some of your references are less appropriate here. Bohm for instance sees the wave function like a hydrodynamic guide-wave for the trajectory of the electrons. So it is as if he really attaches some value to it.

The basic idea of Born is well-used in quantum chemistry where the "square" of the wave-function is used to explain and predict molecular structure and the interaction with light (absorption and fluorescence)

There are many quantities in physics have an imaginary part like dielectric constant and it has a meaning in physics.

Mukhlis

Imaginary quantities in a classical theory are used as simplifications. In QM the wave-function is the fundamental basis of a quantum system.

Mukhlis Ismail,

If I may suggest an approach by Phillipe Grangier:

Contextual objectivity: a realistic interpretation of quantum mechanics

http://cds.cern.ch/record/482106/files/0012122.pdf

Don

I personally are very impressed by the work of Grangier, but then in Quantum Optics. As I mentioned before the area in which the wave-function itself plays a dominant role is that of Quantum Chemistry and I a myself are rereading the book of Pauling and Wilson. This has a very nice introduction for Quantum Mechanics. It starts with a long description of classical Hamiltonian Mechanics.

"INTRODUCTION QUANTUM MECHANICS With Applications to Chemistry. It is free on the web (it dates back to 1935!).

Harry ten Brink,

My suggestions are meant to assist Mukhlis Ismail in approaching a workable conceptual and historical framework from which to understand..."How can i understand that? No physical meaning due to physical meaning?" I have offered suggestions because I experience the difficulty that his questions represent, and not with the intention of instructing or directing the potential answers.

If you are so certain of your own comprehension of quantum mechanics then offer your expertise to Mr Ismail, rather than attempting to correct what you have mistakenly taken to be my referential shortcomings.

We do not agree on Bohm and I would leave it there...agree to disagree.

Don/Mukhlis

I apologise if I gave the impression I was correcting you. The thing is that the question and your answers made me go back to the origin and to read for instance the lecture that Born, the scientist with the concept of the meaning of the wave function, gave on the occasion of his Nobel prize. Furthermore, the textbooks give I think a very good representation of the standard Copenhagen Interpretation of the wave-function.

For instance Merzbacher, free on the web. Feynman in his famous lectures, free on the web. Bohm represents a minority interpretation and his approach does not work in complex systems like molecules.

Mukhlis: I have a direct question to you: which books did you read that did not clarify the meaning of the wave-function? Actually better to call it state-function.

Thank you for the excellent redirection. The issues you raise sound promising for a new thread and question.

Don

Again apologies for a previous "rude" wording. I know that we (the Dutch) and the Swiss are very direct in our language

Thank you for all displacing

Mukhlis

I reread the two books I suggested. Actually I do not find in Feynman a very good description of the meaning of the wave-function. However Merzbacher has an excellent introduction in wave mechanics and there is section 2 of chapter 1 that is called the meaning of the wave-function.

This is the book

Thank you Brink

Classically we know of position, momentum, force, acceleration etc. as physical quantities and we have developed intuitive understanding of these quantities. Classical mechanics is a deterministic theory. When we say force=mass X acceleration, we mean that we can measure acceleration and mass by instruments and take a product. Then measure the acceleration by an instrument, and then see that whether this equation is satisfied.

In quantum mechanics we talk about position, momentum, energy etc of single microscopic particles such as an electron, but is is extremely difficult to observe each single electron in a system and measure their position momentum etc. What we observe in an experiment involves some type of averaging.

Still, it is useful to use our classical terminology in quantum mechanics. Now, the observables are operators and measurements are eigenvalue problems. Consider the example of momentum of an electron. The momentum of a particle, which was an observable in classical mechanics becomes an operator. This operator acts on a function, which is a property of the electron which is under consideration. This function, called the wave function, has the necessary information on the electron under consideration. Therefore we see that the wave function carries a lot of meaning. If you want to know about the angular momentum of this electron, use the operators L2 and LZ . The eigenvalues will give you the answer, but then you again use the wave function as the eigenfunction of your eigenvalue problem.

If you want to know about the position of the electron, then calculate the mod square of the wave function. The result is a real valued function,  which displays a peak at some specific value of position, say x0. You can conclude that the probability of finding the electron at x0 is maximum.

Ref. Feynman lectures Vol 3.

Many thanks to you Biswajoy Brahmachari

First of all, accept that (common sense has no place in quantum mechanics).Second, without probability density the wave diverges and propagates about thousand kilometres in tiny seconds!..think about it and try to accept this!