Time Dependant Hamiltonian Jacob question

In summary, the conversation is about a question given by a professor on a time dependent Hamiltonian, with a function f(t) that has two different forms. The problem is that the material covered in the class, specifically in Chapter 10 of Goldstein, only covers conserved Hamiltonians and there are no notes provided. The person is seeking insight on how to deal with the time dependent function and later states that they have figured it out.
  • #1
Liquidxlax
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Homework Statement



I have a question given to me by my prof that is a time dependent Hamiltonian

H(q,p,t) = g(t)(p2/(2m) + kq2/2)

where f(t) has 2 different forms i need to solve

1) eat 2) cos(gt)

problem is goldstein only covers conserved hamiltonians in chapter 10 for the H-J equations and we have no notes in the class about them. My prof doesn't like to answer questions?

Can someone give me some insight how to deal with the time dependent function?

Homework Equations



H(q, ∂S/∂q , t) + ∂S/∂t = 0 i think... but like i said no material on the time dependance

The Attempt at a Solution

 
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  • #2
it's all right i figured it out
 

1. What is a time dependant Hamiltonian Jacobian?

A time dependant Hamiltonian Jacobian is a mathematical expression that describes the relationship between the position and momentum of a system at a specific point in time. It is derived from the Hamiltonian equations, which are used to describe the motion of particles in a system.

2. How is a time dependant Hamiltonian Jacobian used in physics?

A time dependant Hamiltonian Jacobian is used in physics to understand and predict the behavior of dynamic systems. It is commonly used in quantum mechanics to analyze the time evolution of a system and calculate its energy levels and wavefunctions.

3. What is the difference between a time-independent and time-dependent Hamiltonian Jacobian?

A time-independent Hamiltonian Jacobian describes a system where the Hamiltonian (or energy) of the system does not change over time. On the other hand, a time-dependent Hamiltonian Jacobian describes a system where the Hamiltonian changes over time, often due to external influences.

4. How is a time-dependent Hamiltonian Jacobian calculated?

A time-dependent Hamiltonian Jacobian is calculated using the Hamiltonian equations, which involve taking partial derivatives of the Hamiltonian with respect to the position and momentum variables. This allows for the determination of the equations of motion for a system at a specific point in time.

5. What are some real-world applications of the time-dependent Hamiltonian Jacobian?

The time-dependent Hamiltonian Jacobian has many practical applications, including in the fields of quantum mechanics, molecular dynamics, and celestial mechanics. It is also used in the study of chaotic systems, where small changes in initial conditions can lead to drastically different outcomes over time.

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