# What is the electric field around a quantum particle?

• Starbug
In summary, the conversation discusses the challenges of understanding quantum mechanics, specifically in regards to solving the Schrödinger equation for multi-particle systems. The conversation raises questions about the nature of the electric field and its role as a quantum observable. It is suggested to refer to resources on quantum electrodynamics for further understanding.
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?

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.

## 1. What is an electric field?

An electric field is a physical quantity that describes the influence that an electric charge has on other charges in its vicinity. It is represented by a vector and is measured in units of force per unit charge (N/C).

## 2. How is the electric field around a quantum particle different from a classical particle?

The electric field around a quantum particle is described by quantum mechanics, which takes into account the wave-like nature of these particles. This means that the electric field is not a continuous quantity, but rather exists in discrete packets or quanta. This is in contrast to classical particles where the electric field is continuous.

## 3. Can the electric field around a quantum particle be measured?

Yes, the electric field around a quantum particle can be measured using specialized instruments and techniques. However, due to the inherent uncertainty in quantum mechanics, the exact value of the electric field at a specific point cannot be determined, but rather a probability distribution can be obtained.

## 4. How does the electric field around a quantum particle affect its behavior?

The electric field around a quantum particle can affect its behavior in several ways. It can determine the trajectory of the particle, influence its energy levels, and determine its interactions with other particles. The strength and direction of the electric field can also determine the probability of the particle being found at a certain location.

## 5. Is the electric field around a quantum particle always present?

Yes, the electric field around a quantum particle is always present, even when the particle is at rest. This is because the electric field is an inherent property of the particle itself, and it exists regardless of its motion or interaction with other particles.

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