Có 20+ tài liệu thuộc chủ đề "Vật lý hiện đại"
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1 GVHD: T.S Phạm Thị Minh Hạnh. 2 GVHD: T.S Phạm Thị Minh Hạnh. PHÉP BIẾN ĐỔI LAPLACE TRONG HỆ TỌA ĐỘ DESCARTES. HỆ TỌA ĐỘ CONG. 1.3 Hệ tọa độ cong trực giao. 1.5 Điều kiện cần và đủ để hệ tọa độ cong trực giao. 3 GVHD: T.S Phạm Thị Minh Hạnh. GRADIEN CỦA TRƯỜNG VÔ HƯỚNG TRONG...
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Như chúng ta sẽ thấy ở Chương 2, Einstein đã giải quyết được xung đột đó thông qua thuyết tương đối hẹp của ông, một lý thuyết đã làm đảo lộn những quan niệm của chúng ta về không gian và thời gian. Cũng như thuyết tương đối hẹp, lý thuyết mới này cũng làm đảo lộn những quan niệm...
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The expectation value of the energy in this state is greater than or equal to the ground state energy E 0 : ψ | H ˆ | ψ ≥ E 0 . All particles in nature belong to one of the following classes:. The state vector of N identical bosons is totally symmetric with respect to the exchange of any...
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The neutrino counters have an accuracy of the order of 10% and the energy is E = 4 GeV. Above which distances 12 and 23 of the production point of the neutrinos can one hope to detect oscillations coming from the superpositions 1 ↔ 2 and 2 ↔ 3?. Such neutrinos are produced in the collision of high energy cosmic...
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Relative accuracy ∆ω/ω of a fountain atomic clock as a function of the number of atoms N sent in each pulse. With its own (quartz) clock, it compares the times at which different “clicks”. What is the minimum number of satellites that one must see at a given time in order to be able to position oneself in latitude, in...
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Comparing the values b n of question 3.3 with this experimental result, and recalling the result of a measurement of µ x for these values, explain why this proves that the state vector of a spin-1/2 particle changes sign under a rotation by an odd multiple of 2π.. The intensities at the two counters are. The fact that I 2...
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However the position of the central peak does not depend on the velocity, and it is therefore not shifted if the neutron beam has some velocity dispersion.. On the contrary, in the method of question 4.1.5, the position of the cen- tral peak depends directly on the velocity. A dispersion in v will lead to a corresponding dispersion of the...
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Measuring the Electron Magnetic Moment Anomaly. In the framework of the Dirac equation, the gyromagnetic factor g of the electron is equal to 2. In other words, the ratio between the magnetic moment and the spin of the electron is gq/(2m. q/m, where q and m are the charge and the mass of the particle. When one takes into account...
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H ˆ = ˆ H SS + ˆ H A + ˆ H Z (8.4) in the basis. S, m } of the total spin of the two particles.. Calculate the energy eigenvalues in the presence of the field B. express the corresponding eigenstates in the basis. S, m } of the total spin. Draw qualitatively the variations of the...
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where α is the fine structure constant and c the velocity of light. Energy Loss of Ions in Matter. When a charged particle travels through condensed matter, it loses its kinetic energy gradually by transferring it to the electrons of the medium. In this chapter we evaluate the energy loss of the particle as a function of its mass and...
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The EPR Problem and Bell’s Inequality. When a quantum system possesses more than one degree of freedom, the asso- ciated Hilbert space is a tensor product of the spaces associated to each degree of freedom. 11.1 The Electron Spin. Consider a unit vector u ϕ in the (z, x) plane: u ϕ = cos ϕ u z + sin ϕ...
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Variation of g(θ), as defined in the text. Schr¨ odinger’s Cat. The most famous example is Schr¨ odinger’s “cat paradox” where the cat is in a superposition of the “dead” and “alive” states. They are extremely fragile, and a very weak coupling to the environment suffices to destroy the quantum superposition of the two states | φ a and |...
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The statistical mixture of Bob leads to the same momentum distrib- ution as that measured by Alice: the N/2 oscillators in the state | α all lead to a mean momentum +p 0 , and the N/2 oscillators in the state. In the X variable, the resolution of the detector satisfies δX 1. Alice therefore has a sufficient resolution to...
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σ z b = +1 | B ˆ b | σ z b = +1 = σ z b = +1 | B ˆ b | σ b z = +1 where the spin state of a is irrelevant.. similarly, the case θ a = π/2, θ b = π/2 is identical to θ a = 0, θ b =...
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The expectation value of the number of photons in that state is:. (d) These fields are of the same type as the classical fields considered at the beginning of the problem, with. Therefore the expectation values of the field operators satisfy Maxwell’s equa- tions.. (e) The energy of the classical field can be calculated using the result of ques- tion...
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Express the state | Ψ (t) in terms of the phase states. θ k } of the oscillator D . Write the state | Ψ (t 0 ) of the system.. What is the probability to find the value θ k in a measurement of the phase of the “detector” oscillator D. After this measurement has been performed, what is...
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Section 16.2: Ramsey Fringes. The neutron spin precesses freely between the two cavities during time T , and we obtain. By definition, t 0 = t 1 +T and t 1 = 2t 1 − t 0 +T, therefore the transition matrix in the second cavity is. The probability amplitude for detecting the neutron in state. after the second cavity...
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17.3 Coupling of the Cyclotron and Axial Motions. We now study a method for detecting the cyclotron motion. The coupling is produced by an inhomogeneous magnetic field, and it can be described by the additional term in the Hamiltonian:. Show that the excitation numbers of the cyclotron motion (ˆ n r ) and of the magnetron motion (ˆ n l...