Energy for a non-relativistic particle equation

In summary, the equation for energy of a non-relativistic particle is E = (1/2)mv^2, where E is energy, m is mass, and v is velocity. It is derived from the classical mechanics concept of kinetic energy and can be used for both stationary and moving particles, as long as they are non-relativistic. The units of energy in this equation are joules (J) in the SI system and ergs (erg) in the CGS system. This equation is applicable to all types of non-relativistic particles, including atoms, molecules, and macroscopic objects, as long as they follow classical mechanics principles.
  • #1
ZedCar
354
1
I have an equation for a non-relativistic particle, in relation to quantisation of a particle in a box, which states:

E = (p^2 / 2m) = {(n^2 h^2) / (8 m a^2)}

Should the 'h' (Plancks constant) in this equation be h-bar ?

Thanks.
 
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  • #2
If you wish to write the energy levels with ## \hbar ##, then the equation will look like this $$ E = \frac {n^{2} \hbar ^{2} \pi^{2}} {2m a^{2}} $$ The two expressions are equivalent. The way the equation is derived is by using the relation ## p =\hbar k ##, substituting in ## k = \frac {n \pi} {a} ## and then substituting it into ## E = \frac {p^{2}} {2m}##.
 

1. What is the equation for energy of a non-relativistic particle?

The equation for energy of a non-relativistic particle is given by: E = (1/2)mv^2, where E is energy, m is mass, and v is velocity.

2. How is the equation for energy of a non-relativistic particle derived?

The equation is derived from the classical mechanics concept of kinetic energy, which states that the energy of a particle is proportional to its mass and the square of its velocity.

3. Can this equation be used for both stationary and moving particles?

Yes, this equation can be used for both stationary and moving particles, as long as the particle is non-relativistic (i.e. its velocity is significantly less than the speed of light).

4. What are the units of energy in this equation?

The units of energy in this equation are joules (J) in the SI system and ergs (erg) in the CGS system.

5. Is this equation applicable to all types of particles?

This equation is applicable to all types of non-relativistic particles, including atoms, molecules, and macroscopic objects, as long as they follow classical mechanics principles.

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