Lesson 3.5 – Piecewise Functions
... If the slopes of a continuous function f are closing in on the same finite value from either side of a domain point x = x0, then we say that f is differentiable at x = x0 and that the derivative f ( x0 ) exists. Otherwise, the function is not differentiable at x = x0 and the derivative does not exi ...
... If the slopes of a continuous function f are closing in on the same finite value from either side of a domain point x = x0, then we say that f is differentiable at x = x0 and that the derivative f ( x0 ) exists. Otherwise, the function is not differentiable at x = x0 and the derivative does not exi ...
(Bohr Model And X-Rays) Part-1
... • An electron resolves around the nucleus only in those orbits for which the angular momentum is some integral multiple of L= ...
... • An electron resolves around the nucleus only in those orbits for which the angular momentum is some integral multiple of L= ...
The variational principle and simple properties of the ground
... but due to the fact that ⌿ T is positive everywhere and condition 共13兲, ⌿̃ T should change sign at some point, contrary to what has been shown previously. Therefore, we conclude that the presumed hypothesis is incorrect, and that the ground-state wave function cannot be degenerate. ...
... but due to the fact that ⌿ T is positive everywhere and condition 共13兲, ⌿̃ T should change sign at some point, contrary to what has been shown previously. Therefore, we conclude that the presumed hypothesis is incorrect, and that the ground-state wave function cannot be degenerate. ...
Holonomic quantum computation with neutral atoms
... [1] is a dynamical one: in order to manipulate the quantum state of systems encoding information, local interactions between low dimensional subsystems (qubits) are switched on and off in such a way to enact a sequence of quantum gates. On the other hand, ever since the discovery of the Berry’s phase ...
... [1] is a dynamical one: in order to manipulate the quantum state of systems encoding information, local interactions between low dimensional subsystems (qubits) are switched on and off in such a way to enact a sequence of quantum gates. On the other hand, ever since the discovery of the Berry’s phase ...
Exact reduced dynamics and
... techniques is mathematically simple and physically clear, and allows us to treat systems and environments that could all be strongly coupled ...
... techniques is mathematically simple and physically clear, and allows us to treat systems and environments that could all be strongly coupled ...
Parallel Universes
... Quantum immortality is one of the elements to quantum suicide. If a gun is used measuring quarks, the quarks will decide if the gun shoots depending on what motion they spin. If they spin counter clockwise, the gun will not shoot, even if loaded, making anyone near the gun, immortal to it. This is s ...
... Quantum immortality is one of the elements to quantum suicide. If a gun is used measuring quarks, the quarks will decide if the gun shoots depending on what motion they spin. If they spin counter clockwise, the gun will not shoot, even if loaded, making anyone near the gun, immortal to it. This is s ...
Variations on Quantum Theory
... value for the concrete oscillator, not the Planck constant. When we consider twodimensional ocillators, two types of commutation appear like the commutators for bozons and fermions. I consider also some another aspects of the quantum – classic analogy. I show, there is very much of common details in ...
... value for the concrete oscillator, not the Planck constant. When we consider twodimensional ocillators, two types of commutation appear like the commutators for bozons and fermions. I consider also some another aspects of the quantum – classic analogy. I show, there is very much of common details in ...
9/25 - SMU Physics
... If a particle is confined inside a boundary of finite size, can you be certain about the particle’s velocity at any given time? Why the Bohr’s hydrogen model is flawed? If you have problem in understanding example 4.6, you need to see me in my office hour. ...
... If a particle is confined inside a boundary of finite size, can you be certain about the particle’s velocity at any given time? Why the Bohr’s hydrogen model is flawed? If you have problem in understanding example 4.6, you need to see me in my office hour. ...
Quantum gravity
... For about 70 years, this wave-particle duality was explained by another unsettling tenet of quantum theory - the Heisenberg uncertainty principle. Formulated by Werner Heisenberg in 1927 and recently made more precise, the theory puts an upper limit on knowledge. It says one can never know both the ...
... For about 70 years, this wave-particle duality was explained by another unsettling tenet of quantum theory - the Heisenberg uncertainty principle. Formulated by Werner Heisenberg in 1927 and recently made more precise, the theory puts an upper limit on knowledge. It says one can never know both the ...
Exam #: Printed Name: Signature: PHYSICS
... atomic motion. Suppose that initially each of the two regions contains the same number n of bound surface atoms. a) With the partition in place, find the number of distinct (micro-) states for the total system. b) Now the partition is removed, thus allowing atoms to cross over between the two regions ...
... atomic motion. Suppose that initially each of the two regions contains the same number n of bound surface atoms. a) With the partition in place, find the number of distinct (micro-) states for the total system. b) Now the partition is removed, thus allowing atoms to cross over between the two regions ...
ESSAY 24 : Derivation of the Pauli Exclusion Principle from The
... quantum mechanics. In its simplest form it states that if there is more than one electron in an atom or molecule, no two electrons can have the same n, l, m, j and s quantum numbers. Another way of stating it is that the total wavefunction including spin is antisymmetric with respect to interchange ...
... quantum mechanics. In its simplest form it states that if there is more than one electron in an atom or molecule, no two electrons can have the same n, l, m, j and s quantum numbers. Another way of stating it is that the total wavefunction including spin is antisymmetric with respect to interchange ...
The Future of Computer Science
... Bennett et al. 1997: “Quantum magic” won’t be enough If you throw away the problem structure, and just consider an abstract “landscape” of 2n possible solutions, then even a quantum computer needs ~2n/2 steps to find the correct one (That bound is actually achievable, using Grover’s algorithm!) ...
... Bennett et al. 1997: “Quantum magic” won’t be enough If you throw away the problem structure, and just consider an abstract “landscape” of 2n possible solutions, then even a quantum computer needs ~2n/2 steps to find the correct one (That bound is actually achievable, using Grover’s algorithm!) ...
Chapter 7
... The product of the wavelength and the frequency, though, is a constant. c = l n, where c is the speed of light. Thus, if we know the frequency, we can find the wavelength and vice versa. LEP #1(a). ...
... The product of the wavelength and the frequency, though, is a constant. c = l n, where c is the speed of light. Thus, if we know the frequency, we can find the wavelength and vice versa. LEP #1(a). ...
Quantum Field Theory - Why and When?
... quanta of the vorticity field in a superfluid. So the criterion for when quantum field theory, rather than usual quantum mechanics, must be used is whether or not creation and annihilation processes are important. This again depends on the energy cost, E0 , for creating a new particle. In elementary ...
... quanta of the vorticity field in a superfluid. So the criterion for when quantum field theory, rather than usual quantum mechanics, must be used is whether or not creation and annihilation processes are important. This again depends on the energy cost, E0 , for creating a new particle. In elementary ...
De Broglie waves
... the position and momentum of particles. • If an object is said be at position of x with an uncertainty of Δx, then any simultaneous measurement of the x component of momentum must have an uncertainty Δpx consistent with x px h • It also implies that either wave or particle properties, but not bo ...
... the position and momentum of particles. • If an object is said be at position of x with an uncertainty of Δx, then any simultaneous measurement of the x component of momentum must have an uncertainty Δpx consistent with x px h • It also implies that either wave or particle properties, but not bo ...
... physics majors. Other science or engineering majors with the appropriate background may also find it useful. II. Prerequisites; Physics 325 or permission of the instructor. III. Credit Hours; Three IV. Objectives of the Course; This course is intended to give the student an understanding of the hist ...
The Boltzmann equation
... Time of flight in the hydrodynamic regime Inversion of ellipticity at long times i.e. similar behaviour as for superfluid phases ! ...
... Time of flight in the hydrodynamic regime Inversion of ellipticity at long times i.e. similar behaviour as for superfluid phases ! ...
Physics 880.06: Problem Set 7
... 6. This problem is for edification only: not to be turned in. In class we discussed a SQUID consisting of two Josephson junctions, with critical currents Ic1 and Ic2 . We showed, for the case Ic1 = Ic2 , that the critical current of the SQUID was a periodic function of the flux Φ through the loop wi ...
... 6. This problem is for edification only: not to be turned in. In class we discussed a SQUID consisting of two Josephson junctions, with critical currents Ic1 and Ic2 . We showed, for the case Ic1 = Ic2 , that the critical current of the SQUID was a periodic function of the flux Φ through the loop wi ...
• Quantum physics explains the energy levels of atoms with
... • Quantum physics explains the energy levels of atoms with enormous accuracy. This is possible, since these levels have long lifetime (uncertainty relation for E, t). • Radiation from atoms and molecules enables the most accurate time and length measurements: Atomic clocks • Quantum physics explai ...
... • Quantum physics explains the energy levels of atoms with enormous accuracy. This is possible, since these levels have long lifetime (uncertainty relation for E, t). • Radiation from atoms and molecules enables the most accurate time and length measurements: Atomic clocks • Quantum physics explai ...
Renormalization group
In theoretical physics, the renormalization group (RG) refers to a mathematical apparatus that allows systematic investigation of the changes of a physical system as viewed at different distance scales. In particle physics, it reflects the changes in the underlying force laws (codified in a quantum field theory) as the energy scale at which physical processes occur varies, energy/momentum and resolution distance scales being effectively conjugate under the uncertainty principle (cf. Compton wavelength).A change in scale is called a ""scale transformation"". The renormalization group is intimately related to ""scale invariance"" and ""conformal invariance"", symmetries in which a system appears the same at all scales (so-called self-similarity). (However, note that scale transformations are included in conformal transformations, in general: the latter including additional symmetry generators associated with special conformal transformations.)As the scale varies, it is as if one is changing the magnifying power of a notional microscope viewing the system. In so-called renormalizable theories, the system at one scale will generally be seen to consist of self-similar copies of itself when viewed at a smaller scale, with different parameters describing the components of the system. The components, or fundamental variables, may relate to atoms, elementary particles, atomic spins, etc. The parameters of the theory typically describe the interactions of the components. These may be variable ""couplings"" which measure the strength of various forces, or mass parameters themselves. The components themselves may appear to be composed of more of the self-same components as one goes to shorter distances.For example, in quantum electrodynamics (QED), an electron appears to be composed of electrons, positrons (anti-electrons) and photons, as one views it at higher resolution, at very short distances. The electron at such short distances has a slightly different electric charge than does the ""dressed electron"" seen at large distances, and this change, or ""running,"" in the value of the electric charge is determined by the renormalization group equation.