Search results
Results From The WOW.Com Content Network
The case of a particle in a one-dimensional ring is an instructive example when studying the quantization of angular momentum for, say, an electron orbiting the nucleus. The azimuthal wave functions in that case are identical to the energy eigenfunctions of the particle on a ring.
In quantum mechanics, the case of a particle in a one-dimensional ring is similar to the particle in a box. The particle follows the path of a semicircle from 0 {\displaystyle 0} to π {\displaystyle \pi } where it cannot escape, because the potential from π {\displaystyle \pi } to 2 π {\displaystyle 2\pi } is infinite.
the mass–energy equivalence formula which gives the energy in terms of the momentum and the rest mass of a particle. The equation for the mass shell is also often written in terms of the four-momentum ; in Einstein notation with metric signature (+,−,−,−) and units where the speed of light c = 1 {\displaystyle c=1} , as p μ p μ ≡ p ...
A standard example is the "electron quasiparticle": an electron in a crystal behaves as if it had an effective mass which differs from its real mass. On the other hand, a collective excitation is usually imagined to be a reflection of the aggregate behavior of the system, with no single real particle at its "core".
However the total energy of the particle E and its relativistic momentum p are frame-dependent; relative motion between two frames causes the observers in those frames to measure different values of the particle's energy and momentum; one frame measures E and p, while the other frame measures E ′ and p ′, where E ′ ≠ E and p ′ ≠ p ...
The following derivation [4] makes use of the Trotter product formula, which states that for self-adjoint operators A and B (satisfying certain technical conditions), we have (+) = (/ /), even if A and B do not commute.
The field equations of condensed matter physics are remarkably similar to those of high energy particle physics. As a result, much of the theory of particle physics applies to condensed matter physics as well; in particular, there are a selection of field excitations, called quasi-particles, that can be created and explored. These include:
According to ordinary quantum theory, it is not possible to measure the spin or polarization of a particle directly; instead, the component in one direction is measured; the outcome from a single particle may be 1, meaning that the particle is aligned with the measuring apparatus, or −1, meaning that it is aligned the opposite way. An ...