square of amplitude of quantum wave function refers to volumetric probability distribution of a quantum wave-particle. But what does the real and imaginary parts physically mean? or what does the phase angle physically infer?
You can end up discussing just two things, probability density and phase.
For probability density, just psi(R)psi(R)+psi(I)psi(I)
This is the Born rule.
Phase is only relevant when two waves interfere.
This would be
arc tan (psi(I)/psi(R)) for one wave.
The relevant part would be phase difference between two waves, in interference experiments.
Wave function can be split into absolute value and phase parts by
\psi = |\psi| exp(i phase)
Absolute value |\psi| is related to probability density \rho by \rho=|\psi|^2 while phase part drives mean value of momentum with the same \rho (if phase depends on configuration variable) by
< \psi|p|\psi>=\int \hbar phase' \rho dx+ i \int \psi* \psi' dx
Where is the wave originated from? There is no answer for it!
My perception of universe is a quantum mechanics phenomenon, and space of universe also is special substance that act inside of atom to temperature and pressure. The wave is originated from sun, and space based on temperature is creating Wave. Wave is the source of communication, e.g. all our sense is working with wave. wave in atom exist, and if you consider atom as smart atom, then wave in atom is source of its communication for its integument with other atom. Everything in universe is acting duality, wave-temperature is one of them.
Article How the Language of the Universe Works
From highly feasible explanations of the lift of QM qubits to geometric algebra even subalgebra objects (see the project https://www.researchgate.net/project/Quantum-Computing-with-Geometric-Algebra) it became obvious that, up to scaling factor, wave function must be considered as operator (old dream of P. Dirac) acting on observables, that is very different from conventional QM interpretation. Its “real” part is there the scalar component of the geometric algebra element and the bivector part, which is generalization of formal conventional “imaginary part”, defines the plane where the operator acts in.
The complex number field is intrinsic to the mathematical formulations of quantum mechanics, where complex Hilbert spaces provide the context for one such formulation that is convenient and perhaps most standard. The original foundation formulas of quantum mechanics – the Schrödinger equation and Heisenberg's matrix mechanics – make use of complex numbers.
Dear Sumit Bhowmick, in addition to all the interesting answers posted here previously, probably you would like to look at Quantum Mechanics by Landau and Lifshits, Pergamon, 1965, chapt. on elastic collisions, discussion on pp. 512.
The imaginary part in the exponent determines the lifetime of the state. It is a resonance in a quasi discrete level, also that is the origin of the so-called quasiparticles with a quasi-stationary state.
Important to say that they are solutions of a Schrodinger equation with outgoing spherical waves at infinity, a more real physical system, than those that require the wave function to be finite at infinite.
9 November MMXX
Hi there, P!
I need some advice, please.
I keep getting ERROR WHILE SHARIN PRESENTATION or MESSAGE NOT SENT MESSAGE SENDING FAILED.
Can you explain this for me?
Cordially...
Tonu
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