Calculating Total Energy and Number of States for N Harmonic Oscillators

In summary, an N-harmonic oscillator is a physical system that exhibits oscillatory motion around a stable equilibrium point. It differs from a simple harmonic oscillator in that it has multiple distinct harmonic frequencies, allowing for more complex and varied oscillatory patterns. Some real-life examples include pendulums, springs, and electrical circuits, and its behavior is greatly affected by its initial conditions. N-harmonic oscillators have practical applications in various fields, such as engineering, physics, chemistry, and economics.
  • #1
basma
6
0
I am having this problem in my book:

For a set of N identical harmonic oscillators, the energy for the ith harmonic oscillator is E(i)= (n(i) - 1/2)*h (nu).
(a) What is the total energy of this system?
(b) What is the number of states, Omega (E) , for N=2 and 3?
(c) What is the number of states for a large N.

I thought about the first part. I think I should just add all these energies.

Basma
 
Physics news on Phys.org
  • #2
Any help would be appreciated. I can't even start this problem.

Thanks
 

FAQ: Calculating Total Energy and Number of States for N Harmonic Oscillators

1. What is an N-harmonic oscillator?

An N-harmonic oscillator is a physical system that exhibits oscillatory motion around a stable equilibrium point. It is characterized by a restoring force that is proportional to the displacement from the equilibrium point and follows the harmonic motion equation. The "N" in N-harmonic refers to the number of distinct harmonic frequencies present in the system.

2. How does an N-harmonic oscillator differ from a simple harmonic oscillator?

A simple harmonic oscillator has only one harmonic frequency, whereas an N-harmonic oscillator has multiple distinct harmonic frequencies. This means that an N-harmonic oscillator can exhibit more complex and varied oscillatory patterns, making it a more versatile model for describing physical systems.

3. What are some real-life examples of N-harmonic oscillators?

N-harmonic oscillators can be found in many physical systems, such as pendulums, springs, and electrical circuits. They are also commonly used to model the vibrations of molecules in chemistry and the oscillations of financial markets in economics.

4. How is the behavior of an N-harmonic oscillator affected by its initial conditions?

The initial conditions of an N-harmonic oscillator, such as the initial displacement and velocity, can greatly affect its behavior. These conditions determine the amplitudes and phases of the different harmonic frequencies present in the system, and can result in a wide range of oscillatory patterns.

5. Are there any practical applications for N-harmonic oscillators?

Yes, N-harmonic oscillators have many practical applications in fields such as engineering, physics, chemistry, and economics. They are commonly used to model and analyze the behavior of complex systems, and have also been used to develop technologies such as vibration sensors and frequency filters.

Similar threads

Quantum Harmonic Oscillator, what is #E_0#?
Replies
5
Views
211
Difference between expectation value of ##x## and classical amplitude of oscillation for an harmonic oscillator
Replies
4
Views
1K
Anharmonic Quantum Oscillator
Replies
1
Views
214
Is the Heisenberg Picture Better for a Time-Dependent Hamiltonian?
Replies
4
Views
2K
Partition function for harmonic oscillators
Replies
2
Views
3K
Harmonic potential exercise with perturbation theory
Replies
2
Views
752
Understanding solution to equations of motion of n coupled oscillators
Replies
4
Views
435
QFT for Gifted Amateur - Problem 2.2
Replies
1
Views
1K
Harmonic oscillator with ladder operators - proof using the Sum Rule
Replies
4
Views
2K
What is the Mean Number of Oscillatory Quanta After a Hamiltonian Change?
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top