The Klein-Gordon Equation as a time-symmetric
... the free parameters of the Schrödinger Equation solution But 80 years of experiments say we can’t learn any more information (at one time) than can be encoded by . (Deeply connected with the Uncertainty Principle) Therefore, if we start with the KGE as the master Equation, one gets the axiomatic ...
... the free parameters of the Schrödinger Equation solution But 80 years of experiments say we can’t learn any more information (at one time) than can be encoded by . (Deeply connected with the Uncertainty Principle) Therefore, if we start with the KGE as the master Equation, one gets the axiomatic ...
Polarization statistics
... distributions for the complex amplitudes that depend on a real parameter s including the Q function as the case s 1, the Wigner function as the case s 0 and the P function as the case s 1. From them we have derived the corresponding marginal distributions removing by integvration the other va ...
... distributions for the complex amplitudes that depend on a real parameter s including the Q function as the case s 1, the Wigner function as the case s 0 and the P function as the case s 1. From them we have derived the corresponding marginal distributions removing by integvration the other va ...
Chapter 5 : Electrons in Atoms
... size of the orbital. Orbitals for which n = 2 are larger than those for which n = 1, for example. Because they have opposite electrical charges, electrons are attracted to the nucleus of the atom. Energy must therefore be absorbed to excite an electron from an orbital in which the electron is close ...
... size of the orbital. Orbitals for which n = 2 are larger than those for which n = 1, for example. Because they have opposite electrical charges, electrons are attracted to the nucleus of the atom. Energy must therefore be absorbed to excite an electron from an orbital in which the electron is close ...
Department of Physics Indian Institute of Technology Kanpur
... 1. Sadri Hassani, Mathematical Physics: a modern introduction to its foundations (Springer) 2. Arfken, Weber- Mathematical Methods for Physicists (Academic Press) 3. Tulsi Dass and S. K. Sharma, Mathematical methods in Classical and Quantum Physics (University Press) ...
... 1. Sadri Hassani, Mathematical Physics: a modern introduction to its foundations (Springer) 2. Arfken, Weber- Mathematical Methods for Physicists (Academic Press) 3. Tulsi Dass and S. K. Sharma, Mathematical methods in Classical and Quantum Physics (University Press) ...
Thermal Physics PH2001
... • If it can be assumed that the number of available states is much larger than the number of particles then the probability of finding any two particles in the same state is very low. We then have N! different ways of assigning those states to the particles. But as the particles are indistinguishabl ...
... • If it can be assumed that the number of available states is much larger than the number of particles then the probability of finding any two particles in the same state is very low. We then have N! different ways of assigning those states to the particles. But as the particles are indistinguishabl ...
Chapter 1 Review of Quantum Mechanics
... which correspond to different states of the particle’s motion. Therefore, people sometime use these discrete set of quantum numbers to characterize state of the particle’s motion. A state function such as Φk (r) can not be measured directly. It has a meaning of probability : its modular |Φk (r)|2 gi ...
... which correspond to different states of the particle’s motion. Therefore, people sometime use these discrete set of quantum numbers to characterize state of the particle’s motion. A state function such as Φk (r) can not be measured directly. It has a meaning of probability : its modular |Φk (r)|2 gi ...
Quantum Field Theory and Mathematics
... properties they satisfy. If this can be done, this will be good not only for mathematicians but also for physicists. This is because these general properties of quantum field theory are not yet written down in textbooks in any concise manner, even within theoretical physics. It is true that these pr ...
... properties they satisfy. If this can be done, this will be good not only for mathematicians but also for physicists. This is because these general properties of quantum field theory are not yet written down in textbooks in any concise manner, even within theoretical physics. It is true that these pr ...
The quantum phases of matter
... LS Cable, a South Korean company based in Anyang-si near Seoul, has ordered three million metres of superconducting wire from US firm American Superconductor in Devens, Massachusetts. Jason Fredette, managing director of corporate communications at the company, says that LS Cable will use the wire ...
... LS Cable, a South Korean company based in Anyang-si near Seoul, has ordered three million metres of superconducting wire from US firm American Superconductor in Devens, Massachusetts. Jason Fredette, managing director of corporate communications at the company, says that LS Cable will use the wire ...
Quantum key distribution
Quantum key distribution (QKD) uses quantum mechanics to guarantee secure communication. It enables two parties to produce a shared random secret key known only to them, which can then be used to encrypt and decrypt messages. It is often incorrectly called quantum cryptography, as it is the most well known example of the group of quantum cryptographic tasks.An important and unique property of quantum key distribution is the ability of the two communicating users to detect the presence of any third party trying to gain knowledge of the key. This results from a fundamental aspect of quantum mechanics: the process of measuring a quantum system in general disturbs the system. A third party trying to eavesdrop on the key must in some way measure it, thus introducing detectable anomalies. By using quantum superpositions or quantum entanglement and transmitting information in quantum states, a communication system can be implemented which detects eavesdropping. If the level of eavesdropping is below a certain threshold, a key can be produced that is guaranteed to be secure (i.e. the eavesdropper has no information about it), otherwise no secure key is possible and communication is aborted.The security of encryption that uses quantum key distribution relies on the foundations of quantum mechanics, in contrast to traditional public key cryptography which relies on the computational difficulty of certain mathematical functions, and cannot provide any indication of eavesdropping at any point in the communication process, or any mathematical proof as to the actual complexity of reversing the one-way functions used. QKD has provable security based on information theory, and forward secrecy.Quantum key distribution is only used to produce and distribute a key, not to transmit any message data. This key can then be used with any chosen encryption algorithm to encrypt (and decrypt) a message, which can then be transmitted over a standard communication channel. The algorithm most commonly associated with QKD is the one-time pad, as it is provably secure when used with a secret, random key. In real world situations, it is often also used with encryption using symmetric key algorithms like the Advanced Encryption Standard algorithm. In the case of QKD this comparison is based on the assumption of perfect single-photon sources and detectors, that cannot be easily implemented.