Four Classes of Quantum Mechanical Effects are Independent?

[Islam Hassan]

Are the four classes of quantum mechanical phenomena for which classical physics cannot account independent of one another or can one derive one or more phenomena from other(s)? These according to the Wiki are:

• Principle of uncertainty;
• Wave-particle duality;
• Quantisation of certain physical phenomena; and
• Quantum entanglement.

IH

 

[DrClaude]

All of these derive from more fundamental aspects of quantum mechanics.

One way to consider it is by starting from the postulates of quantum mechanics:

1. Associated with any particle moving in a conservative field of force is a wave function which determines everything that can be known about the system.
2. With every physical observable q there is associated an operator Q, which when operating upon the wavefunction associated with a definite value of that observable will yield that value times the wavefunction.
3. Any operator Q associated with a physically measurable property q will be Hermitian.
4. The set of eigenfunctions of operator Q will form a complete set of linearly independent functions.
5. For a system described by a given wavefunction, the expectation value of any property q can be found by performing the expectation value integral with respect to that wavefunction.
6. The time evolution of the wavefunction is given by the time dependent Schrödinger equation.

The uncertainty principle is a consequence of 2 and the fact that some operators Q do not commute with each other. The "wave-particle duality," which is an outdated concept, is a consequence of 1, 2 5, and 6 (the system and its evolution is obtained from a wave equation, but observations are particle-like). Quantization is related to the discreteness of some observables or boundary conditions of the wave equation.

Quantum entanglement is something else, as it requires more than one particle, and is related to the rules coverning composite systems and the superposition principle, the latter being also a consequence of 6 by the fact that the Schrödinger equation is a linear equation.

 

[Islam Hassan]

Thanx DrClaude, much appreciated