The free particle in spherical coordinates

In summary, a free particle in spherical coordinates is a theoretical model used in physics to study the behavior of particles without external forces. Its motion is described using the simplified Schrödinger equation, with the main differences between spherical and Cartesian coordinates being the way position is described and the components of motion considered. Spherical coordinates have physical significance in understanding the particle's position and direction of motion. The energy of a free particle in spherical coordinates is related to its motion through the Schrödinger equation and determines its probability distribution.
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loewenzahn
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the free particle in spherical coordinates
Hi!
I'm studying Shankar's Principle of quantum mechanics
I didn't get the last conclusion, can someone help me understand it, please. Where did the l over rho come from?

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  • #2
Expand the 2nd line. (And btw, if you still don't get it, show your attempt.)
 
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Likes vanhees71 and Nugatory

Related to The free particle in spherical coordinates

1. What is the free particle in spherical coordinates?

The free particle in spherical coordinates is a theoretical concept in physics that describes the movement and behavior of a particle in a three-dimensional space, using spherical coordinates (radius, polar angle, and azimuthal angle) instead of Cartesian coordinates (x, y, z).

2. How is the free particle in spherical coordinates different from the free particle in Cartesian coordinates?

The main difference between the two is the coordinate system used to describe the particle's position and motion. In spherical coordinates, the particle's position is described using a radial distance from the origin, an angle from the z-axis, and an angle from the x-axis. In Cartesian coordinates, the position is described using the x, y, and z coordinates.

3. What is the advantage of using spherical coordinates to describe the free particle?

Spherical coordinates are particularly useful when dealing with problems that have spherical symmetry, such as those involving gravitational or electrostatic forces. They also simplify certain calculations, such as finding the distance between two points or the volume of a sphere.

4. Can the free particle in spherical coordinates be used to describe the behavior of real particles?

No, the free particle in spherical coordinates is a simplified model used in theoretical physics to understand the behavior of particles in a three-dimensional space. In reality, particles are subject to various forces and interactions, making their behavior much more complex.

5. How is the free particle in spherical coordinates related to quantum mechanics?

In quantum mechanics, the free particle in spherical coordinates is used to describe the behavior of particles at the atomic and subatomic level. It is a fundamental concept in understanding the wave-particle duality of quantum objects and plays a crucial role in many quantum mechanical equations and models.

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