What is the electric field around a quantum particle?

[Starbug]

Beginning another attempt in my amateurish efforts to understand quantum mechanics, I suddenly realized there was a basic issue I find completely unclear.

When we solve the SE for an interesting system we first need to input a potential, which is usually some function of the spatial coordinates. For example courses often start by looking at a particle in a box, and then of course the hydrogen atom. But when we solve the hydrogen atom as a single particle state in a fixed Coloumb potential this must just be an approximation. Since in fact the thing it's orbiting must also be represented by a wavefunction. So in fact we need a multi-particle state. Now I know we must be able to deal with multi-particle states since I have vague memories knocking around of doing the helium atom using perturbation theory, but I'm having some conceptual trouble getting my head around the nature of the electric field around things that don't have a definite position. Is the E-field at some point in space also a quantum observable with some probability of being this or this, depending on the different weighting of all the combinations of possible positions of all charged particles?

 

[xantox]

The electric field is a quantum field. See http://en.wikipedia.org/wiki/Quantum_electrodynamics and http://www.vega.org.uk/video/subseries/8

 

[denian]

The electric field around a quantum particle is a complex concept that requires a deep understanding of quantum mechanics. In general, the electric field is a fundamental force that acts on charged particles, and it is described by classical electromagnetism. However, in the quantum realm, the concept of a definite position and a definite electric field becomes blurred.

In quantum mechanics, a particle is described by a wavefunction, which represents the probability of finding the particle at a certain position. As you correctly pointed out, when we solve the Schrodinger equation for a system, we need to input a potential, which can be thought of as the external forces acting on the particle. In the case of a hydrogen atom, the potential is the Coulomb potential due to the positively charged nucleus.

However, in reality, the electron in the hydrogen atom is not orbiting a fixed Coulomb potential, as you mentioned. Instead, the electron and the nucleus are both described by wavefunctions, and their interaction can be described using quantum mechanics. In this case, the electric field around the electron is not a definite quantity, but rather it is described by a probability distribution. The electric field at a certain point in space is a quantum observable, but it can only be measured with a certain probability.

To fully understand the nature of the electric field around a quantum particle, one must study the concept of superposition and entanglement in quantum mechanics. These concepts allow for the existence of multiple states and probabilities for a single particle, and they play a crucial role in understanding the electric field around a quantum particle.

In summary, the electric field around a quantum particle is not a simple concept and requires a deep understanding of quantum mechanics. It is not a definite quantity, but rather it is described by a probability distribution that is affected by the wavefunctions of all particles involved in the system.