Classical harmonic oscillator with quantum energy spectrum
... It is well-known, the quantum systems, including atoms, harmonic oscillator etc., have a discrete set of stationary states with discrete energy levels. The stationary state with the least energy is the ground state; all other stationary states are excited. Being in one of such states, the system ha ...
... It is well-known, the quantum systems, including atoms, harmonic oscillator etc., have a discrete set of stationary states with discrete energy levels. The stationary state with the least energy is the ground state; all other stationary states are excited. Being in one of such states, the system ha ...
Part 1 - SCIPP
... The four momentum of the system prior to the collision is given by pµb = (E + m, px , 0, 0) ...
... The four momentum of the system prior to the collision is given by pµb = (E + m, px , 0, 0) ...
The role of the electromagnetic field in the formation of domains in
... the matter components on an extended space-time region. Furthermore, we will discuss extended domains exhibiting in their fundamental states non-vanishing order parameters, whose existence is not included in the Lagrangian. The interest in the general problem of the stability of mesoscopic and macro ...
... the matter components on an extended space-time region. Furthermore, we will discuss extended domains exhibiting in their fundamental states non-vanishing order parameters, whose existence is not included in the Lagrangian. The interest in the general problem of the stability of mesoscopic and macro ...
Generalized Classical Electrodynamics
... gradient of the Whittaker electric potential waves are longitudinal electric waves, and the time derivative of the Whittaker electric potential waves are scalar field waves. Tom Bearden's reference to “Whittaker's infolded hidden EM structure in the scalar potential” is mathematically wrong, because ...
... gradient of the Whittaker electric potential waves are longitudinal electric waves, and the time derivative of the Whittaker electric potential waves are scalar field waves. Tom Bearden's reference to “Whittaker's infolded hidden EM structure in the scalar potential” is mathematically wrong, because ...
using standard pra s
... these energy separations. So far, precision measurements of S-T anticrossing separations were performed on the 1s3d configuration using laser spectroscopy 关1兴 and on the 1s5l configurations using level-crossing and radio-frequency spectroscopy 关2兴. In combination with accurately known zero-field fin ...
... these energy separations. So far, precision measurements of S-T anticrossing separations were performed on the 1s3d configuration using laser spectroscopy 关1兴 and on the 1s5l configurations using level-crossing and radio-frequency spectroscopy 关2兴. In combination with accurately known zero-field fin ...
A Primer on Resonances in Quantum Mechanics
... and satisfying purely outgoing conditions are known as Gamow-Siegert functions [1, 2]. These solutions represent a special case of scattering states for which the 'capture' of the incident wave produces delays in the scattered wave. The 'time of capture' can be connected with the lifetime of a decay ...
... and satisfying purely outgoing conditions are known as Gamow-Siegert functions [1, 2]. These solutions represent a special case of scattering states for which the 'capture' of the incident wave produces delays in the scattered wave. The 'time of capture' can be connected with the lifetime of a decay ...
Modified Weak Energy Condition for the Energy Momentum Tensor
... of parameters by making use of conformal invariance [6,7]. The lengthy algebra involved in some of the three-point function computations is reduced significantly by restricting the state so that the three points in the correlation function lie on a straight line. The positivity inequalities obtained ...
... of parameters by making use of conformal invariance [6,7]. The lengthy algebra involved in some of the three-point function computations is reduced significantly by restricting the state so that the three points in the correlation function lie on a straight line. The positivity inequalities obtained ...
Quantum fluctuations and thermal dissipation in higher derivative
... of a massive charged (quark like) particle at the boundary. What we would essentially study is the linear response of the system when perturbed due to some external (electrical) force. In order to compute the two point correlation function, we would assume the so-called fluctuation dissipation theor ...
... of a massive charged (quark like) particle at the boundary. What we would essentially study is the linear response of the system when perturbed due to some external (electrical) force. In order to compute the two point correlation function, we would assume the so-called fluctuation dissipation theor ...
Killing time - Department of Physics
... have fixed the gauge in the calculation of the previous subsection because ¢ is implicitly assumed to be propagated instantaneously. No delta function is included in the integrand to make the calculation advanced or retarded. It appears that we have adopted the Coulomb gauge IV. A = 0]. We will expl ...
... have fixed the gauge in the calculation of the previous subsection because ¢ is implicitly assumed to be propagated instantaneously. No delta function is included in the integrand to make the calculation advanced or retarded. It appears that we have adopted the Coulomb gauge IV. A = 0]. We will expl ...
T. Szarek and P.F. Dunn, An Apparatus to Determine the Pull
... C2 is a coefficient that encompasses the effect of relative humidity. C3 is the pull-off force reduction factor derived by Cheng, Dunn, and Brach (2002) that accounts for the effect of the asperity roughness height, that is, the surface roughness between the particle and electrode surface. C1 and C3 ...
... C2 is a coefficient that encompasses the effect of relative humidity. C3 is the pull-off force reduction factor derived by Cheng, Dunn, and Brach (2002) that accounts for the effect of the asperity roughness height, that is, the surface roughness between the particle and electrode surface. C1 and C3 ...
Microcanonical distributions for quantum systems
... statistical theory is lost, and one is left with a conceptual foundation for the equilibrium physics of large quantum systems that is in many respects less than satisfactory. There has, however, been one modern development in quantum theory that may allow for a way forward with this issue. This is t ...
... statistical theory is lost, and one is left with a conceptual foundation for the equilibrium physics of large quantum systems that is in many respects less than satisfactory. There has, however, been one modern development in quantum theory that may allow for a way forward with this issue. This is t ...
Casimir effect
In quantum field theory, the Casimir effect and the Casimir–Polder force are physical forces arising from a quantized field. They are named after the Dutch physicist Hendrik Casimir.The typical example is of two uncharged metallic plates in a vacuum, placed a few nanometers apart. In a classical description, the lack of an external field means that there is no field between the plates, and no force would be measured between them. When this field is instead studied using the QED vacuum of quantum electrodynamics, it is seen that the plates do affect the virtual photons which constitute the field, and generate a net force—either an attraction or a repulsion depending on the specific arrangement of the two plates. Although the Casimir effect can be expressed in terms of virtual particles interacting with the objects, it is best described and more easily calculated in terms of the zero-point energy of a quantized field in the intervening space between the objects. This force has been measured and is a striking example of an effect captured formally by second quantization. However, the treatment of boundary conditions in these calculations has led to some controversy.In fact, ""Casimir's original goal was to compute the van der Waals force between polarizable molecules"" of the metallic plates. Thus it can be interpreted without any reference to the zero-point energy (vacuum energy) of quantum fields.Dutch physicists Hendrik B. G. Casimir and Dirk Polder at Philips Research Labs proposed the existence of a force between two polarizable atoms and between such an atom and a conducting plate in 1947, and, after a conversation with Niels Bohr who suggested it had something to do with zero-point energy, Casimir alone formulated the theory predicting a force between neutral conducting plates in 1948; the former is called the Casimir–Polder force while the latter is the Casimir effect in the narrow sense. Predictions of the force were later extended to finite-conductivity metals and dielectrics by Lifshitz and his students, and recent calculations have considered more general geometries. It was not until 1997, however, that a direct experiment, by S. Lamoreaux, described above, quantitatively measured the force (to within 15% of the value predicted by the theory), although previous work [e.g. van Blockland and Overbeek (1978)] had observed the force qualitatively, and indirect validation of the predicted Casimir energy had been made by measuring the thickness of liquid helium films by Sabisky and Anderson in 1972. Subsequent experiments approach an accuracy of a few percent.Because the strength of the force falls off rapidly with distance, it is measurable only when the distance between the objects is extremely small. On a submicron scale, this force becomes so strong that it becomes the dominant force between uncharged conductors. In fact, at separations of 10 nm—about 100 times the typical size of an atom—the Casimir effect produces the equivalent of about 1 atmosphere of pressure (the precise value depending on surface geometry and other factors).In modern theoretical physics, the Casimir effect plays an important role in the chiral bag model of the nucleon; in applied physics, it is significant in some aspects of emerging microtechnologies and nanotechnologies.Any medium supporting oscillations has an analogue of the Casimir effect. For example, beads on a string as well as plates submerged in noisy water or gas illustrate the Casimir force.