Document
... At this point, either Ms. Jones or Mr. Brown would have just left, and the other one would still be in service. The exponential is memoryless. It is the same as if service for that person were just starting at this point. The probability that the remaining person finishes before Smith leaves must eq ...
... At this point, either Ms. Jones or Mr. Brown would have just left, and the other one would still be in service. The exponential is memoryless. It is the same as if service for that person were just starting at this point. The probability that the remaining person finishes before Smith leaves must eq ...
Lecture notes, part 2
... = 0. If all these states are also normalized, they are said to be “orthonormal”. Case 2: degenerate. En can equal Em even if n 6= m. The proof is more complicated than the non-degenerate case. We need to use the GramSchmitt orthogonalization procedure to construct orthogonal states by taking appropr ...
... = 0. If all these states are also normalized, they are said to be “orthonormal”. Case 2: degenerate. En can equal Em even if n 6= m. The proof is more complicated than the non-degenerate case. We need to use the GramSchmitt orthogonalization procedure to construct orthogonal states by taking appropr ...
Mar 11/02 Matter Waves
... at a time at random intervals • interference fringes still build up • raises the question: if the photons move through the apparatus one at a time, through which slit does the photon pass? • How does a given photon know that there is another slit? • Can a single photon pass through both slits and in ...
... at a time at random intervals • interference fringes still build up • raises the question: if the photons move through the apparatus one at a time, through which slit does the photon pass? • How does a given photon know that there is another slit? • Can a single photon pass through both slits and in ...
The Future of Computer Science
... (you knew it was coming) Quantum mechanics: “Probability theory with minus signs” (Nature seems to prefer it that way) ...
... (you knew it was coming) Quantum mechanics: “Probability theory with minus signs” (Nature seems to prefer it that way) ...
Observables and Measurements
... and is represented by a Hermitean operator. Thus, if a system is in a given state (a pure state |φi or a mixed state ρ), one can determine expectation values and uncertainties in this observable. These properties refer to the expected outcomes of an ensemble of measurements (i.e., measuring many ide ...
... and is represented by a Hermitean operator. Thus, if a system is in a given state (a pure state |φi or a mixed state ρ), one can determine expectation values and uncertainties in this observable. These properties refer to the expected outcomes of an ensemble of measurements (i.e., measuring many ide ...
Uncertainty Principle
... the superposed wave Φ(x, t) = Φ1 (x, t) + Φ2 (x, t) and I(x, t) = Φ(x, t)Φ(x, t) = Φ(x, t)Φ∗ (x, t), since we assumed Φ was real. ...
... the superposed wave Φ(x, t) = Φ1 (x, t) + Φ2 (x, t) and I(x, t) = Φ(x, t)Φ(x, t) = Φ(x, t)Φ∗ (x, t), since we assumed Φ was real. ...
Statistical Thermodynamics
... • The most “disordered” macrostate is the state with the highest probability. • The macrostate with the highest thermodynamic probability will be the observed equilibrium state of the system. • The statistical model suggests that systems tend to change spontaneously from states with low thermodynam ...
... • The most “disordered” macrostate is the state with the highest probability. • The macrostate with the highest thermodynamic probability will be the observed equilibrium state of the system. • The statistical model suggests that systems tend to change spontaneously from states with low thermodynam ...
Key Concepts for Exam #2
... If the frequency of the light is below the threshold frequency, then each individual photon lacks enough energy to remove an electron from the metal and no electrons are released from the metal. Blackbody Radiation c T max 2 where the constant c 2 1.44 10 2 m ...
... If the frequency of the light is below the threshold frequency, then each individual photon lacks enough energy to remove an electron from the metal and no electrons are released from the metal. Blackbody Radiation c T max 2 where the constant c 2 1.44 10 2 m ...
Chapter 5
... RANDOM VARIABLE – a numerical variable whose value depends on the outcome of a random experiment. A random variable may be discrete or continuous. Ex. A) Select a month at random. Are the following random variables discrete or continuous? What are some possible values for each? (a) n = the number of ...
... RANDOM VARIABLE – a numerical variable whose value depends on the outcome of a random experiment. A random variable may be discrete or continuous. Ex. A) Select a month at random. Are the following random variables discrete or continuous? What are some possible values for each? (a) n = the number of ...
Computation, Quantum Theory, and You
... • But probably still not Satisfiability • Contrast: Nonlinear quantum mechanics would put Satisfiability and even harder problems in polynomial time (Abrams and Lloyd 1998) ...
... • But probably still not Satisfiability • Contrast: Nonlinear quantum mechanics would put Satisfiability and even harder problems in polynomial time (Abrams and Lloyd 1998) ...
Limitations of Quantum Advice and One-Way
... (Won’t say any more about this one) Ambainis: Suppose Alice has x,yFp and Bob has a,bFp. They want to know whether yax+b. 1-way quantum communication complexity? ...
... (Won’t say any more about this one) Ambainis: Suppose Alice has x,yFp and Bob has a,bFp. They want to know whether yax+b. 1-way quantum communication complexity? ...
Common Core Math 7 EOG Questions- Statistics and Probability 1. A
... Which statement about the two high-school seniors must be true? A. Senior A must have a larger box. B. Senior B must have a larger box. C. Senior A must have a higher median. D. Senior B must have a greater range. ...
... Which statement about the two high-school seniors must be true? A. Senior A must have a larger box. B. Senior B must have a larger box. C. Senior A must have a higher median. D. Senior B must have a greater range. ...
Alg2 Notes 8.7.notebook
... the graph to estimate the probability that Jamie will be able to drive more than 450 miles on her next tank of gas. There are about 100 squares under the graph ...
... the graph to estimate the probability that Jamie will be able to drive more than 450 miles on her next tank of gas. There are about 100 squares under the graph ...
Lecture 8: Period Finding: Simon`s Problem over ZN 1 Problem
... Let us briefly recall what generally happens when we use this trick. If we have a function g : G → C such that Ex∈R G [|g(x)|2 ] = 1, where G is either Zn2 or ZN , then the following is a valid quantum state: 1 X ...
... Let us briefly recall what generally happens when we use this trick. If we have a function g : G → C such that Ex∈R G [|g(x)|2 ] = 1, where G is either Zn2 or ZN , then the following is a valid quantum state: 1 X ...
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.