Applications of Number Theory in Computer Science Curriculum
... The problem: A transmitter sends binary bits For a single bit, there is a probability 0.8 that 0 is sent and probability 0.2 that 1 is sent When a 0 is sent, a 0 will be received with probability 0.8 When a 1 is sent, the 1 will be received with probability ...
... The problem: A transmitter sends binary bits For a single bit, there is a probability 0.8 that 0 is sent and probability 0.2 that 1 is sent When a 0 is sent, a 0 will be received with probability 0.8 When a 1 is sent, the 1 will be received with probability ...
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
... 12) Evaluate ( um, x un) where un’s are the eigenfunctions of a linear harmonic oscillator. 13) Prove that “the momentum operator in quantum mechanics is the generator of infinitesimal translations”. 14) (a) Prove that ( σ.A) (σ.B) = A.B + i σ. ( A xB) where σ’s are the Pauli spin matrices , if the ...
... 12) Evaluate ( um, x un) where un’s are the eigenfunctions of a linear harmonic oscillator. 13) Prove that “the momentum operator in quantum mechanics is the generator of infinitesimal translations”. 14) (a) Prove that ( σ.A) (σ.B) = A.B + i σ. ( A xB) where σ’s are the Pauli spin matrices , if the ...
slides
... mechanics defines a probability distribution for the full trajectory. Notice that the velocity equation is simply v= J/p, where J is the quantum probability current and p is the quantum probability density. It follows from the quantum continuity equation that if the distribution of the configuration ...
... mechanics defines a probability distribution for the full trajectory. Notice that the velocity equation is simply v= J/p, where J is the quantum probability current and p is the quantum probability density. It follows from the quantum continuity equation that if the distribution of the configuration ...
Quantum Mechanics as dissolver of the sensate universe: this is
... But the nature is dual: wave and particle; the particle interpretation is still there Even as early as the 17th century, we see indications of the unsuspected trajectory that physics and mathematics were taking, which would prove the undoing of the sensate world view. In 1801, the British physicist ...
... But the nature is dual: wave and particle; the particle interpretation is still there Even as early as the 17th century, we see indications of the unsuspected trajectory that physics and mathematics were taking, which would prove the undoing of the sensate world view. In 1801, the British physicist ...
7Copenhagen
... m = 9.11 x 10-31 kg (.14 x 10-9 m)p > (6.626 x 10-34 Js)/2 p = 7.5 x 10-25 kg m/s p = mv (7.5 x 10-25 kg m/s) = (9.11 x 10-31 kg)v v = 8.3 x 105 m/s v = 8.3 x 105 m/s ...
... m = 9.11 x 10-31 kg (.14 x 10-9 m)p > (6.626 x 10-34 Js)/2 p = 7.5 x 10-25 kg m/s p = mv (7.5 x 10-25 kg m/s) = (9.11 x 10-31 kg)v v = 8.3 x 105 m/s v = 8.3 x 105 m/s ...
Lecture 22
... We examine a series of (independent, identical) experiments (for example, experiments to measure a certain unknown quantity V ). Let M1 , M2 , . . . denote the actual results obtained which are assumed to be numerical for simplicity. We want to examine the probability p of obtaining the result that ...
... We examine a series of (independent, identical) experiments (for example, experiments to measure a certain unknown quantity V ). Let M1 , M2 , . . . denote the actual results obtained which are assumed to be numerical for simplicity. We want to examine the probability p of obtaining the result that ...
Transition Probability (Fidelity) and its Relatives
... What can be done if the system is in a mixed state with density operator ρ1 and we like to prepare another mixed state, ρ2 , by a measurement? This task cannot be performed within the system itself2 . We have to leave the system based on H and have to go to larger systems in which one can perform ap ...
... What can be done if the system is in a mixed state with density operator ρ1 and we like to prepare another mixed state, ρ2 , by a measurement? This task cannot be performed within the system itself2 . We have to leave the system based on H and have to go to larger systems in which one can perform ap ...
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MTH 150 SURVEY OF MATHEMATICS
... an empirical probability of 0 means that the event never occurred, but could occur in the future; ...
... an empirical probability of 0 means that the event never occurred, but could occur in the future; ...
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.