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... In mechanics and field theory (both classical and quantum), there are two main languages - Lagrangian and Hamiltonian. In the classical setting, the Lagrangian language is the language of vari-ational calculus (i.e. one studies extremals of the action functional), while the Hamiltonian language is t ...
... In mechanics and field theory (both classical and quantum), there are two main languages - Lagrangian and Hamiltonian. In the classical setting, the Lagrangian language is the language of vari-ational calculus (i.e. one studies extremals of the action functional), while the Hamiltonian language is t ...
Chapter 8 The quantum theory of motion
... Classical mechanics It is impossible for a particle to surmount over a barrier with potential energy high than its kinetic energy. Quantum mechanics If the barrier is thin and the barrier energy is not infinite, particles have the probability to penetrate into the potential region forbidden by class ...
... Classical mechanics It is impossible for a particle to surmount over a barrier with potential energy high than its kinetic energy. Quantum mechanics If the barrier is thin and the barrier energy is not infinite, particles have the probability to penetrate into the potential region forbidden by class ...
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... Any wave-function can be the stationary wave-function of the system only if it is a solution of this energy-eigenvalue equation, thus the energy has a certain, well defined value. Heisenberg’s uncertainty principle There is a fundamental limit to the precision with which certain pairs of physical pr ...
... Any wave-function can be the stationary wave-function of the system only if it is a solution of this energy-eigenvalue equation, thus the energy has a certain, well defined value. Heisenberg’s uncertainty principle There is a fundamental limit to the precision with which certain pairs of physical pr ...
Creating Entanglement
... The Hamiltonian The Hamiltonian operator is a function of operators concerning degrees of freedom (dynamical variables) of the system. Eg. if quantum information is encoded in positions x1 and x2 of two particles, then with … representing other relevant operators. Momentum p is conjugate to p ...
... The Hamiltonian The Hamiltonian operator is a function of operators concerning degrees of freedom (dynamical variables) of the system. Eg. if quantum information is encoded in positions x1 and x2 of two particles, then with … representing other relevant operators. Momentum p is conjugate to p ...
LanZ_0112_eps(1).
... This thesis explores Feynman’s idea of quantum simulations by using ultracold quantum gases. In the first part of the thesis we develop a general method applicable to atoms or molecules or even nanoparticles, to decelerate a hot fast gas beam to zero velocity by using an optical cavity. This deceler ...
... This thesis explores Feynman’s idea of quantum simulations by using ultracold quantum gases. In the first part of the thesis we develop a general method applicable to atoms or molecules or even nanoparticles, to decelerate a hot fast gas beam to zero velocity by using an optical cavity. This deceler ...
Anomaly of non-locality and entanglement in teaching quantum
... told that whenever Alice measures either ~/2 or −~/2, she instantly knows that Bob will obtain the opposite result upon measuring the other particle’s spin along the same direction. Then it is mentioned that the two particles are entangled or, in other words, they display a quantum correlation which ...
... told that whenever Alice measures either ~/2 or −~/2, she instantly knows that Bob will obtain the opposite result upon measuring the other particle’s spin along the same direction. Then it is mentioned that the two particles are entangled or, in other words, they display a quantum correlation which ...
