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What is the expression for the l2 operator in spherical coordinates and how does it affect the quantum state of a particle in a spherically symmetric potential?
The expression for the (l2) operator in spherical coordinates is ( -hbar2 left( frac1sintheta fracpartialpartialtheta left( sintheta fracpartialpartialtheta right) frac1sin2theta fracpartial2partialphi2 right) ). This operator measures the square of the angular momentum of a particle in a spherically symmetric potential. It quantifies the total angular momentum of the particle and its projection along a specific axis. The eigenvalues of the (l2) operator correspond to the possible values of the total angular momentum quantum number (l), which in turn affects the quantum state of the particle in the potential.
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What is the expression for the metric tensor in spherical coordinates?
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What is the metric in spherical coordinates?
The metric in spherical coordinates is a mathematical formula that describes the distance between points in a three-dimensional space using the radial distance, azimuthal angle, and polar angle. It is used to calculate distances and areas in spherical geometry.
