Action (physics)
The effect is in physics as a quantity with the dimension of energy times time or pulse times path length. This dimension is equal to the angular momentum. However, the effect is a scalar, the angular momentum of an axial vector.
The equations of motion of physical systems arising from the principle of least action.
According to quantum mechanics effects as well as angular momentum is not any amount, but are always integer or half-integer multiples of Planck's constant.
Equations of motion
The equations that describes the theoretical physics particles and their interactions follow from the principle of least action. In mechanics, for example, the actually traversed paths are distinguished by the fact that in their case the effect is compared with other railways is at a minimum.
To Newtonian mechanics, the effect is the time integral over the difference between the kinetic and potential energy. Each path, which is traversed from a starting point to an end point in time is associated with an effect:
The Lagrangian is, for example, a particle of mass moving in the potential,
The difference between kinetic and potential energy. Thus, the effect has the dimension of energy times time. Among all the possible paths that run through initially and finally, the physical paths have the smallest (specifically, stationary ) effect and therefore satisfy the Euler -Lagrange equation
The equation of motion of the particle is not.
Just as the equations of Newtonian mechanics can also be the equations of relativistic mechanics, the Maxwell equations of electrodynamics, the Einstein equations of general relativity and the equations of the standard model of elementary interactions from the condition deduced that an action has a stationary value.
Sommerfeld quantization Bohr -
Before one could describe the behavior of atoms N with quantum mechanics, Bohr and Sommerfeld have the spectra of simple atoms by the Bohr model of the atom explains ( "older quantum mechanics "). Spectral lines occur there as energy differences of two to " discrete " electron orbits. The drilling Sommerfeld quantization rule requested by the orbit of the electron around the nucleus, that not only the equation of motion, but for each round in addition
Must apply. Here, the pulse and the place that is run through. This line integral has the dimension of angular momentum as a place times pulse and is an effect, is the Planck constant. The effect of each stationary electron orbits in the atom is quantized so, it enters the quantum of action only as an integral multiple of Planck's on.
Uncertainty principle
In systems that need to be described with quantum mechanics, can often be the results of measurements impossible to predict, but only the probabilities for specific test results. The variation of the results about its mean is called blur. The Heisenberg uncertainty principle states that the product of spatial and momentum uncertainty can not be less than half of the reduced Planck's constant: