Geometric Algebra
... How many space dimensions do we have? • The existence of five regular solids implies three dimensional space(6 in 4D, 3 > 4D) • Gravity and EM follow inverse square laws to very high precision. Orbits(Gravity and Atomic) not stable with more than 3 D. • Tests for extra dimensions failed, must be su ...
... How many space dimensions do we have? • The existence of five regular solids implies three dimensional space(6 in 4D, 3 > 4D) • Gravity and EM follow inverse square laws to very high precision. Orbits(Gravity and Atomic) not stable with more than 3 D. • Tests for extra dimensions failed, must be su ...
What`s the big idea? - Perimeter Institute
... no electromagnetic waves would be emitted, and the atom would be stable. Why? Because waves are created by things that oscillate, and there’s nothing oscillating about a rotating ring. A rotating ring of charge would create static electric and magnetic fields, but no electromagnetic waves that would ...
... no electromagnetic waves would be emitted, and the atom would be stable. Why? Because waves are created by things that oscillate, and there’s nothing oscillating about a rotating ring. A rotating ring of charge would create static electric and magnetic fields, but no electromagnetic waves that would ...
Arthur-Merlin and Black-Box Groups in Quantum
... But what about proving non-membership in H? Fact: For some groups G (even abelian groups), there’s no small NP proof (or even MA proof) for non-membership (Non-membership can always be proved in AM, using ...
... But what about proving non-membership in H? Fact: For some groups G (even abelian groups), there’s no small NP proof (or even MA proof) for non-membership (Non-membership can always be proved in AM, using ...
The Learnability of Quantum States
... optics experiment still collapse the polynomial hierarchy? Main Result: Yes, assuming two plausible conjectures about permanents of random matrices (the “PCC” and the “PGC”) Particular experiment we have in mind: Take a system of n identical photons with m=O(n2) modes. Put each photon in a known mod ...
... optics experiment still collapse the polynomial hierarchy? Main Result: Yes, assuming two plausible conjectures about permanents of random matrices (the “PCC” and the “PGC”) Particular experiment we have in mind: Take a system of n identical photons with m=O(n2) modes. Put each photon in a known mod ...
Paper
... distributions of a set of random variables RV. Suppose that by some reasons (e.g. technological or social, or economical, or political) we are not able to perform measurements of the whole collection of random variables ξ ∈ RV. Thus we are not able to obtain the complete statistical description of s ...
... distributions of a set of random variables RV. Suppose that by some reasons (e.g. technological or social, or economical, or political) we are not able to perform measurements of the whole collection of random variables ξ ∈ RV. Thus we are not able to obtain the complete statistical description of s ...
Here is the whole problem. Assume body temperatures are normally
... Solution. Denote the body temperature by X. Then by hypothesis, X follows normal distribution with mean of 98.2 and a standard dev. of 0.62, i.e., X ~ N (98.2,0.62 2 ) . Now we need to find the probability ...
... Solution. Denote the body temperature by X. Then by hypothesis, X follows normal distribution with mean of 98.2 and a standard dev. of 0.62, i.e., X ~ N (98.2,0.62 2 ) . Now we need to find the probability ...
Document
... ability of the Feynman-Kac formula to "see topology" (in much more complex situations) lies at the foundation of many interrelations between geometry and quantum field theory. Remark. It should be noted that the contributions of topologically nontrivial maps from the source circle to the target circ ...
... ability of the Feynman-Kac formula to "see topology" (in much more complex situations) lies at the foundation of many interrelations between geometry and quantum field theory. Remark. It should be noted that the contributions of topologically nontrivial maps from the source circle to the target circ ...
YMS Chapter 7 Random Variables
... Q3. The distribution of the number of successes out of n trials (with probability of success p on each trial) is the ______ _______. Q4. If someone has 51 socks in a drawer, with 1/3 red and 2/3 black, and the person grabs a handful of 5 of them, and counts the number of black, will the results of s ...
... Q3. The distribution of the number of successes out of n trials (with probability of success p on each trial) is the ______ _______. Q4. If someone has 51 socks in a drawer, with 1/3 red and 2/3 black, and the person grabs a handful of 5 of them, and counts the number of black, will the results of s ...
251y0242
... III. Do at least 4 of the following 6 Problems (at least 12 each) (or do sections adding to at least 48 points Anything extra you do helps, and grades wrap around) . Show your work! Please indicate clearly what sections of the problem you are answering! If you are following a rule like E ax aEx ...
... III. Do at least 4 of the following 6 Problems (at least 12 each) (or do sections adding to at least 48 points Anything extra you do helps, and grades wrap around) . Show your work! Please indicate clearly what sections of the problem you are answering! If you are following a rule like E ax aEx ...
GAUGE FIELD THEORY Examples
... Spin-zero particles of charge e, mass m, are incident on a one-dimensional rectangular potential barrier of height V such that eV > 2mc2 . Show that when the particles have total energy E = eV /2 the barrier is perfectly transparent, independent of its thickness. Find ρ and Jx inside the barrier in ...
... Spin-zero particles of charge e, mass m, are incident on a one-dimensional rectangular potential barrier of height V such that eV > 2mc2 . Show that when the particles have total energy E = eV /2 the barrier is perfectly transparent, independent of its thickness. Find ρ and Jx inside the barrier in ...
Time in Quantum Theory
... →Hilbert space. The Hilbert space basis |q> diagonalizes an appropriate observable Q. The time dependence of a quantum state is in fact meaningful only relative to such a fixed basis, as demonstrated by means of the wave function in the above definition. In non-relativistic quantum mechanics, the ti ...
... →Hilbert space. The Hilbert space basis |q> diagonalizes an appropriate observable Q. The time dependence of a quantum state is in fact meaningful only relative to such a fixed basis, as demonstrated by means of the wave function in the above definition. In non-relativistic quantum mechanics, the ti ...
Document
... PROBLEM 7 A sodium atom is in one of the states labeled ''Lowest excited levels". It remains in that state for an average time of 1.610-8 s before it makes a transition back to a ground state, emitting a photon with wavelength 589.0 nm and energy 2.105 eV. What is the uncertainty in energy of that ...
... PROBLEM 7 A sodium atom is in one of the states labeled ''Lowest excited levels". It remains in that state for an average time of 1.610-8 s before it makes a transition back to a ground state, emitting a photon with wavelength 589.0 nm and energy 2.105 eV. What is the uncertainty in energy of that ...
Quantum Mechanics I, Sheet 1, Spring 2015
... (e) If T̂L f (x) = f (x − L), how does T̂L act of f˜(k), the fourier transform of f (x)? In other words, what modification of f˜(k) corresponds to translating f (x) by L? (f) Use parts (c) and (e) to determine how D̂ acts on f˜(k). (g) Use the definition of the position operator and the definition o ...
... (e) If T̂L f (x) = f (x − L), how does T̂L act of f˜(k), the fourier transform of f (x)? In other words, what modification of f˜(k) corresponds to translating f (x) by L? (f) Use parts (c) and (e) to determine how D̂ acts on f˜(k). (g) Use the definition of the position operator and the definition o ...
Review for Exam 1
... Remember that the limits and the volume element depend on the system that we are describing. For instance for a 1 dimensional particle in a box, d is simply dx and the limits on the integral are over the dimensions of the box, (i.e. 0 to L). Is the denominator in this expression always necessary? ...
... Remember that the limits and the volume element depend on the system that we are describing. For instance for a 1 dimensional particle in a box, d is simply dx and the limits on the integral are over the dimensions of the box, (i.e. 0 to L). Is the denominator in this expression always necessary? ...
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.