Planck constant

Planck's quantum of action, or Planck's constant , is the relationship between the energy ( ) and frequency ( ) of a photon, according to the formula $E = h \cdot f$ . The same relationship holds in general between the energy of a particle or physical system and the frequency of its quantum mechanical phase.

The discovery of the quantum of action by Max Planck in 1899 and 1900 founded quantum physics. The quantum of action links properties that were previously attributed in classical physics either only to particles or only to waves. Thus it is the basis of the wave-particle duality of modern physics.

At that time, Planck considered the quantum of action to be the third of the fundamental natural constants of physics, along with the gravitational constant and the speed of light. Together, these constants form the basis of Planck's natural system of units. He gave the name "elementary quantum of action" to the constant he discovered, because it plays a decisive role in "elementary oscillation processes" and, according to the definition (see above), results as a quotient of an energy and a frequency, which is why it has the same dimension as the physical quantity effect.

Commemorative plaque - Humboldt-Universität zu Berlin

Definition

Planck's quantum of action is, for every physical system that can oscillate harmonically, always the same ratio of the smallest possible energy conversion to the oscillation frequency. Larger energy conversions are only possible if they are integer multiples of this smallest energy amount. However, this quantization of energy is practically not noticeable in macroscopic systems.

Moreover, for any physical system, is the ratio of its total energy content to the frequency of its quantum mechanical phase.

Planck's quantum of action has the dimension of energy times time, which is called the effect. However, the effect is not quantized, as one might conclude from the name.

The quantum of action gets its universal meaning from its appearance in the basic equations of quantum physics (Schrödinger equation, Heisenberg equation of motion, Dirac equation).

Some general consequences

Any harmonic oscillation (with frequency , angular frequency ω $\omega =2\pi f$ ) can absorb or release energy only in discrete amounts that $\Delta E = h f \equiv \hbar \omega$ are integer multiples of the quantum of oscillation Δ
Any physical system can $\hbar \equiv \tfrac{h}{2\pi}$ change its angular momentum (more precisely, the projection of the angular momentum vector ${\vec {J}}$ onto any straight line) only by integer multiples of
Each physical system with momentum is associated with a matter wave of wavelength λ $\lambda = \tfrac{h}{p}$
For any physical system, energy and angular frequency ω $\omega$ of its quantum mechanical phase satisfy the equation $E = \hbar \omega$ .
Each two variables of a physical system which are canonically conjugate to each other (e. g., location and momentum of a particle, or generalized location and generalized momentum, e. g., angle of rotation and angular momentum) satisfy an uncertainty relation according to which they cannot both have well-defined values simultaneously in any state of the system. Rather, for the scatterers σ of $\sigma_x,\, \sigma_p$ the values of both variables: σ $\sigma_x\cdot\sigma_p\ge\tfrac{\hbar}{2}$ .

Questions and Answers

Q: What is the Planck constant?

A: The Planck constant is a fundamental physical constant that says how much the energy of a photon increases when the frequency of its electromagnetic wave increases by 1. It is written as h and expressed in joule seconds (J⋅s) or (N⋅m⋅s) or (kg⋅m2⋅s−1).

Q: Who was it named after?

A: The Planck constant was named after physicist Max Planck.

Q: What are the dimensions of physical action for this constant?

A: The dimensions of physical action for the Planck constant are energy multiplied by time, or momentum multiplied by distance.

Q: How is it expressed in SI units?

A: In SI units, the Planck constant is expressed in joule seconds (J⋅s) or (N⋅m⋅s) or (kg⋅m2⋅s−1).

Q: What measurements can be calculated using this quantity?

A: Scientists have used this quantity to calculate measurements like the Planck length and the Planck time.

Q: What equation describes magnetron W and electron L?

A: Magnetron W=Wb/2P Electron L=4C/3X = 25e/3 =(13U1d).