Particle moving in x and theta

In summary, the conversation discusses the derivation of the Hamiltonian for a particle moving in a potential in the x direction while also rotating with an angle of theta. The speaker has attempted to use the TISE and angular momentum operator in 2d space, but has been unsuccessful. They suggest parametrising the particle's motion into either spherical polar or cartesian coordinates as a potential solution.
  • #1
NEWO
95
0
How would one derive the hamiltonian for a particle moving in a potential in the x direction whilst also rotating with an angle of theta??

I have tried deriving it the same way as the TISE using the angular momentum operator in 2d space but to no avail

basically the particle is moving through a potential with an integer spin.

would appreciate any pointers

Newo
 
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  • #2
x and theta are not independent coordinates - there are spherical polar and cartesian hamiltonians, but deriving a hybrid of both would be obscene.

Parametrise the particle's motion into either spherical polar or cartesian coordinates, first.
 

FAQ: Particle moving in x and theta

1. What is a particle moving in x and theta?

A particle moving in x and theta is a type of motion where the particle's position is described by two coordinates, x and theta. X represents the particle's position along a linear path, while theta represents the angle of rotation from a fixed point.

2. How is the motion of a particle in x and theta different from other types of motion?

In a particle moving in x and theta, the particle's position is not only determined by its location along a path, but also by its rotation. This type of motion is more complex and requires a different set of equations to describe and analyze.

3. What factors affect the motion of a particle in x and theta?

The motion of a particle in x and theta is affected by several factors, including the particle's initial position, velocity, and acceleration, as well as any external forces acting on the particle.

4. How is the motion of a particle in x and theta described mathematically?

The motion of a particle in x and theta can be described mathematically using equations such as the displacement equation x = x0 + v0t + 1/2at^2 and the rotational displacement equation theta = theta0 + omega0t + 1/2alpha*t^2, where x0 and theta0 represent the initial position and angle, v0 and omega0 represent the initial velocity and angular velocity, a and alpha represent the acceleration and angular acceleration, and t is time.

5. What applications does the study of particles moving in x and theta have?

The study of particles moving in x and theta has many applications, including in engineering, robotics, and physics. It can help us understand and predict the motion of objects in complex systems, such as rotating machinery and robotic arms.

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