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staraptor
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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>?
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.
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.
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.
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.
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.