# Expectation of position in a 2D system

• staraptor
In summary, the expectation of position in a 2D system is a measure of the average location of a particle in a two-dimensional space, calculated by taking into account the probability of finding the particle at each point in the space and weighting it by the position value. It is calculated using the formula: E(x) = ∫∫xψ*(x,y)ψ(x,y)dxdy and provides valuable information about the average location of a particle in a two-dimensional space. It can change depending on the properties of the system and is related to the uncertainty principle, as there is always a certain degree of uncertainty in its position.
staraptor
How does on calculate the expectation of the position operator x in a 2D infinite potential well (in the xy plane)? Do we only work with the Psi to the Hamiltonian in that particular coordinate when finding <Psi|x|Psi>?

You calculate
$$\langle x \rangle = \iint \psi^*(x,y)\,x\,\psi(x,y)\,dx\,dy$$

Could you explain this please? Where does the double intergral come from?

The expectation value of the position operator x in a 2D infinite potential well is calculated by taking the inner product of the position operator with the wave function Psi in the xy plane. This is represented by <Psi|x|Psi>. However, it is important to note that the expectation value is not solely dependent on the wave function in that particular coordinate. The Hamiltonian operator also plays a crucial role in determining the expectation value. Therefore, when calculating <Psi|x|Psi>, both the wave function and the Hamiltonian should be taken into consideration. Additionally, it is important to keep in mind that the expectation value is a statistical quantity and may vary for different measurements of the position in the 2D system.

## What is the expectation of position in a 2D system?

The expectation of position in a 2D system is a measure of the average location of a particle in a two-dimensional space. It is calculated by taking into account the probability of finding the particle at each point in the space and weighting it by the position value.

## How is the expectation of position calculated in a 2D system?

The expectation of position in a 2D system is calculated using the formula: E(x) = ∫∫xψ*(x,y)ψ(x,y)dxdy, where ψ*(x,y) is the complex conjugate of the wave function and ψ(x,y) is the wave function describing the particle's position in the two-dimensional space.

## What is the significance of the expectation of position in a 2D system?

The expectation of position in a 2D system provides valuable information about the average location of a particle in a two-dimensional space. It is a fundamental concept in quantum mechanics and is used to calculate other important quantities such as momentum and energy.

## How does the expectation of position change in a 2D system?

The expectation of position in a 2D system can change depending on the properties of the system, such as the shape of the potential barrier or the strength of the magnetic field. It can also change over time as the particle's wave function evolves according to the Schrödinger equation.

## What is the relationship between the uncertainty principle and the expectation of position in a 2D system?

The uncertainty principle states that the more precisely we know the position of a particle, the less precisely we can know its momentum, and vice versa. The expectation of position in a 2D system is related to this principle, as it represents the most probable location of the particle, but there is always a certain degree of uncertainty in its position.

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