2.4.8 Kullback-Leibler Divergence
... know limp→0 p log p = 0. However, when p ̸= 0 but q = 0, DKL (p||q) is defined as ∞. This means that if one event e is possible (i.e., p(e) > 0), and the other predicts it is absolutely impossible (i.e., q(e) = 0), then the two distributions are absolutely different. However, in practice, two distribu ...
... know limp→0 p log p = 0. However, when p ̸= 0 but q = 0, DKL (p||q) is defined as ∞. This means that if one event e is possible (i.e., p(e) > 0), and the other predicts it is absolutely impossible (i.e., q(e) = 0), then the two distributions are absolutely different. However, in practice, two distribu ...
Particle on a Sphere
... Spherical Polar Coordinates = most efficient way to describe position of particle on sphere ...
... Spherical Polar Coordinates = most efficient way to describe position of particle on sphere ...
Molekylfysik - Leiden Univ
... (operator)(function)=(constant)×(same function) The eigenvalue is the energy E. The set of eigenvalues are the only values that the energy can have (quantization). The eigenfunctions of the Hamiltonian operator H are the wavefunctions of the system. To each eigenvalue corresponds a set of ei ...
... (operator)(function)=(constant)×(same function) The eigenvalue is the energy E. The set of eigenvalues are the only values that the energy can have (quantization). The eigenfunctions of the Hamiltonian operator H are the wavefunctions of the system. To each eigenvalue corresponds a set of ei ...
Exponential complexity and ontological theories of quantum
... Quantum MC: one does not evaluate the evolution of the multi-particle wave-function, but the averages over a finite number of realizations in a suitable “small” sampling space. Necessary condition for a good QMC method: the dimensionality of the sampling space must grow polynomially with the physica ...
... Quantum MC: one does not evaluate the evolution of the multi-particle wave-function, but the averages over a finite number of realizations in a suitable “small” sampling space. Necessary condition for a good QMC method: the dimensionality of the sampling space must grow polynomially with the physica ...
Quantum1
... •Describes the time evolution of your wavefunction. •Takes the place of Newton’s laws and conserves energy of the system. •Since “particles” aren’t particles but wavicles, it won’t give us a precise position of an individual particle, but due to the statistical nature of things, it will precisely de ...
... •Describes the time evolution of your wavefunction. •Takes the place of Newton’s laws and conserves energy of the system. •Since “particles” aren’t particles but wavicles, it won’t give us a precise position of an individual particle, but due to the statistical nature of things, it will precisely de ...
Notes on Quantum Mechanics - Department of Mathematics
... good enough to measure these two physical quantities simultaneously, it is a basic fact about the quantum mechanical nature of the system itself. Here’s why. As we’ve seen, measuring a physical quantity amounts to finding the eigenvalues of an operator. For self-adjoint operators, this amounts to fi ...
... good enough to measure these two physical quantities simultaneously, it is a basic fact about the quantum mechanical nature of the system itself. Here’s why. As we’ve seen, measuring a physical quantity amounts to finding the eigenvalues of an operator. For self-adjoint operators, this amounts to fi ...
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. ...
Lecture 1 - Particle Physics Group
... Given the list of particles and vertices which exist in a certain theory, (e.g. the SM) we can use FDs to find out all the processes which are allowed by the theory, and make rough estimates of their relative probability. Every vertex and particle corresponds to a term in the Lagrangian (the formula ...
... Given the list of particles and vertices which exist in a certain theory, (e.g. the SM) we can use FDs to find out all the processes which are allowed by the theory, and make rough estimates of their relative probability. Every vertex and particle corresponds to a term in the Lagrangian (the formula ...
qm2 - Michael Nielsen
... 2. Given an information processing task – data compression, information transmission, teleportation; and 3. Given a criterion for success; We ask the question: How much of 1 do I need to achieve 2, while satisfying 3? Pursuing this question in the quantum case has led to, and presumably will continu ...
... 2. Given an information processing task – data compression, information transmission, teleportation; and 3. Given a criterion for success; We ask the question: How much of 1 do I need to achieve 2, while satisfying 3? Pursuing this question in the quantum case has led to, and presumably will continu ...
Entropic Dynamics: A hybrid-contextual theory of Quantum Mechanics
... a contradiction due to the fact that not all of the elements in Mermin’s square commute. Quantum Mechanical formalism and experiment agrees with (22) and not with (23) and thus (19) must be thrown out. Bell makes the good point that it may be overconstraining for the valuation to produce identical v ...
... a contradiction due to the fact that not all of the elements in Mermin’s square commute. Quantum Mechanical formalism and experiment agrees with (22) and not with (23) and thus (19) must be thrown out. Bell makes the good point that it may be overconstraining for the valuation to produce identical v ...
Probability amplitude
In quantum mechanics, a probability amplitude is a complex number used in describing the behaviour of systems. The modulus squared of this quantity represents a probability or probability density.Probability amplitudes provide a relationship between the wave function (or, more generally, of a quantum state vector) of a system and the results of observations of that system, a link first proposed by Max Born. Interpretation of values of a wave function as the probability amplitude is a pillar of the Copenhagen interpretation of quantum mechanics. In fact, the properties of the space of wave functions were being used to make physical predictions (such as emissions from atoms being at certain discrete energies) before any physical interpretation of a particular function was offered. Born was awarded half of the 1954 Nobel Prize in Physics for this understanding (see #References), and the probability thus calculated is sometimes called the ""Born probability"". These probabilistic concepts, namely the probability density and quantum measurements, were vigorously contested at the time by the original physicists working on the theory, such as Schrödinger and Einstein. It is the source of the mysterious consequences and philosophical difficulties in the interpretations of quantum mechanics—topics that continue to be debated even today.