Quantum Mechanics: What is Quanta?

[narrator]

Hi, I've been on the other PF forums for some months, where QM is often mentioned and I assumed I had some basic understanding of it, but I thought I would come here to clarify. I read http://en.wikipedia.org/wiki/Quantum_mechanics" on it and I'm still unsure if I have it right or even complete.

From what I have read, using my own words, QM is about discrete particles and how their internal energy is affected/used/conserved, and/or what that energy is at any instance in time, (allowing for the uncertainty principle). Following on from this, I read that Planck considers waves to be made up of small packets of this quanta. The way I visualized this is like a fog, that when examined closely is made up of tiny droplets of water, each droplet being a packet of many water molecules. Is this what is meant by quanta in QM, that each packet in a wave is a discrete packet of particles, spatially separate from the next packet? And by wave, I imagine that to mean like a beam of light or heat from the sun.

 

[cbetanco]

No, particles are not like droplets in a fog. What they mean by quanta is discrete values for some observable, but I think this is misleading. Quantum mechanics assigns to each physical system (en electron, and atom, a collection of electrons or atoms, or the whole universise, depending on what you want to define as zour closed system) a vector that is infinite dimensional, which represents the current state of the system. Each component of the vector (which lives in an infinite dimensional space) represents a paticular "pure" state of the system (typically referred to as eigenstates). We can try to visualize this in bz taking the analogy in 3d. Let's say an electron (all by iteself) is our physical system and is assigned the state (1,0,1), where the components are x,y,z respectively (not spatial coordinates!). This means that is is really in a little bit of state x, not at all in state y, and a little in state z. Now if you go an measure this electron you will either measure it to be in state x or z with equal probablility (50% and 50% in this paticular case)since it is "pointing" equally in either direction. This is how one really does quantum mechanics, not with waves or quanta. In its most general formulation, quantum mechanics is a theory of operators (representing observables like energy, momentum, position, etc.) acting on vectors that live in an infinite dimensional complex vector space (usuallz referred to as Hilbert space), not of waves or particles or "quanta". I know this sounds confusing, but if you learn some linear algebra, you will know what I mean.

 

[juanrga]

Hi, I've been on the other PF forums for some months, where QM is often mentioned and I assumed I had some basic understanding of it, but I thought I would come here to clarify. I read http://en.wikipedia.org/wiki/Quantum_mechanics" on it and I'm still unsure if I have it right or even complete.

From what I have read, using my own words, QM is about discrete particles and how their internal energy is affected/used/conserved, and/or what that energy is at any instance in time, (allowing for the uncertainty principle). Following on from this, I read that Planck considers waves to be made up of small packets of this quanta. The way I visualized this is like a fog, that when examined closely is made up of tiny droplets of water, each droplet being a packet of many water molecules. Is this what is meant by quanta in QM, that each packet in a wave is a discrete packet of particles, spatially separate from the next packet? And by wave, I imagine that to mean like a beam of light or heat from the sun.

No. QM is about the motion of quantum systems. Quantum systems do not need to be discrete. There exists the QM of continuum objects (e.g. fields).

QM is not about internal energy. In fact the usual Hamiltonian for an atom consists of kinetic energy (K) and external potential energy (V) terms but not of internal energy (U) term.

The rest about waves, fog, tiny droplets of water,... is also incorrect. Moreover, it is very misleading to believe that quantum wavefunctions are as optical waves. And in modern formulations of QM the term «wavefunction» is substituted by state (e.g. when using Dirac kets).