## What is the partition function of harmonic oscillator?

We derive the partition function of the one-body and two-body systems of classical noncommutative harmonic oscillator in two dimensions. Then, we employ the path integral approach to the quantum non- commutative harmonic oscillator and derive the partition function of the both systems at finite temperature.

**What is classical partition function?**

the classical partition function match the quantum one. This will define a quantum-mechanical cell in the phase space of a. classical particle. Show that this quantum-mechanical aspect does not contribute into the internal energy and heat capacity of. the classical particles.

**What is classical harmonic oscillator?**

In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force F proportional to the displacement x: where k is a positive constant.

### What is the partition function for microcanonical ensemble?

An important point about the canonical ensemble is that we derived a result about the system only. The partition function is a sum over microstates of the system. Pk is the probability of nding the system in microstate k when it is in equilibrium at a temperature T no matter what it is in contact with.

**What do you mean by partition function?**

In physics, a partition function describes the statistical properties of a system in thermodynamic equilibrium. Partition functions are functions of the thermodynamic state variables, such as the temperature and volume.

**What is the difference between classical harmonic oscillator and quantum harmonic oscillator?**

The energy spacing is equal to Planck’s energy quantum. The ground state energy is larger than zero. This means that, unlike a classical oscillator, a quantum oscillator is never at rest, even at the bottom of a potential well, and undergoes quantum fluctuations.

## What is the use of harmonic oscillator?

Simple Harmonic Oscillator Applications Simple Harmonic Oscillator is a spring-mass system. It is applied in Clocks as an oscillator, in guitar, violin. It is also seen in the Car-shock absorber where springs are attached to the car wheel to ensure the smoother ride.

**What is the formula for partitions?**

A partition of a number is any combination of integers that adds up to that number. For example, 4 = 3+1 = 2+2 = 2+1+1 = 1+1+1+1, so the partition number of 4 is 5. It sounds simple, yet the partition number of 10 is 42, while 100 has more than 190 million partitions.