2010 midterm exam solutions
... b) What would a measurement of the z-component of angular momentum, Lz , yield? The eigenvalues of Lz are lmz , thus we would measure −4l c) What would a measurement of the x-component of angular momentum, Lx , yield? Since the state is not in an eigenfunction of the Lx angular momentum, the result ...
... b) What would a measurement of the z-component of angular momentum, Lz , yield? The eigenvalues of Lz are lmz , thus we would measure −4l c) What would a measurement of the x-component of angular momentum, Lx , yield? Since the state is not in an eigenfunction of the Lx angular momentum, the result ...
Solution of the Radial Schrödinger Equation for
... Barakat, T. 2006. The asymptotic iteration method for the eigenenergies of the Schrödinger equation with the potential V(r) ≤ -Z/r + gr + λr2. Journal of Physics A: Mathematical and General 39(4): 823-831. Bayrak, O. and Boztosun I. 2006. Arbitrary ℓ-state solutions of the rotating Morse potential b ...
... Barakat, T. 2006. The asymptotic iteration method for the eigenenergies of the Schrödinger equation with the potential V(r) ≤ -Z/r + gr + λr2. Journal of Physics A: Mathematical and General 39(4): 823-831. Bayrak, O. and Boztosun I. 2006. Arbitrary ℓ-state solutions of the rotating Morse potential b ...
Quantum computing
... Turing machine [3], and its practical effectiveness was shown by Deutsch [4]. We considered a few aspects of quantum computing in connection with the time series analysis and its numerical implementation. Shor’s integer factorization algorithm and Quantum Fourier Transform [5, 6] were selected for s ...
... Turing machine [3], and its practical effectiveness was shown by Deutsch [4]. We considered a few aspects of quantum computing in connection with the time series analysis and its numerical implementation. Shor’s integer factorization algorithm and Quantum Fourier Transform [5, 6] were selected for s ...
1 Classical Mechanics
... atomic spectral lines, the spectral distribution of black body radiation, chemical reactions, etc. Nevertheless, classical and quantum mechanics are closely connected. Just as geometrical optics can be regarded as the short wavelength limit of wave optics, so classical mechanics can be regarded as t ...
... atomic spectral lines, the spectral distribution of black body radiation, chemical reactions, etc. Nevertheless, classical and quantum mechanics are closely connected. Just as geometrical optics can be regarded as the short wavelength limit of wave optics, so classical mechanics can be regarded as t ...
Physics 2170
... They proposed a way out: Electrons actually always know their spin in every direction but experiments can only get the limited knowledge allowed by quantum mechanics. A better theory would allow one to get access to this information. This is called a hidden variable theory. In 1964, J.S Bell proved ...
... They proposed a way out: Electrons actually always know their spin in every direction but experiments can only get the limited knowledge allowed by quantum mechanics. A better theory would allow one to get access to this information. This is called a hidden variable theory. In 1964, J.S Bell proved ...
dreams of a finite theory - Indico
... number of space-time dimensions For superstrings 9 space and 1 time coordinates are needed for quantum consistency Rather than a killer this is now seen as an opportunity: if 6 of the 9 spatial dimensions are tiny they can provide a new mechanism to generate gauge interactions (of the GUT type) a ...
... number of space-time dimensions For superstrings 9 space and 1 time coordinates are needed for quantum consistency Rather than a killer this is now seen as an opportunity: if 6 of the 9 spatial dimensions are tiny they can provide a new mechanism to generate gauge interactions (of the GUT type) a ...
Summer Work
... 3. The number of protons in one atom of an element determines the atom’s __________________ , and the number of electrons determines ___________________ of an element. 4. The atomic number tells you the number of ______________________ in one atom of an element. It also tells you the number of _____ ...
... 3. The number of protons in one atom of an element determines the atom’s __________________ , and the number of electrons determines ___________________ of an element. 4. The atomic number tells you the number of ______________________ in one atom of an element. It also tells you the number of _____ ...
Orthogonal polynomials, special functions and mathematical physics
... group the solution of which are given by the associated orthogonal polynomials. The class of quantum integrable systems associated with root systems was introduced by Olshanetsky and Perelomov as a generalization of the Calogero- Sutherland systems [12]. For the potential v(q) = k(k − 1)/(sinq)2 the ...
... group the solution of which are given by the associated orthogonal polynomials. The class of quantum integrable systems associated with root systems was introduced by Olshanetsky and Perelomov as a generalization of the Calogero- Sutherland systems [12]. For the potential v(q) = k(k − 1)/(sinq)2 the ...
The Pauli Principle
... More on Fermions and Bosons • The prediction that even a macroscopic number of bosons can occupy one state: A Bose-Einstein condensate was shown experimentally in 1995 and won Cornelle, Ketterle and Wieman the 2001 Nobelprize. • The properties of bosons also explains that certain liquids, e.g., liqu ...
... More on Fermions and Bosons • The prediction that even a macroscopic number of bosons can occupy one state: A Bose-Einstein condensate was shown experimentally in 1995 and won Cornelle, Ketterle and Wieman the 2001 Nobelprize. • The properties of bosons also explains that certain liquids, e.g., liqu ...
Many-body Quantum Mechanics
... the method of using annihilation and creation operators acting on a Fock space as ”second quantization”. As should be clear from the above, this terminology is misleading in the sense that ψ̂ is not a once more quantized version of the wave function, but an object which is directly (or via a Fourier ...
... the method of using annihilation and creation operators acting on a Fock space as ”second quantization”. As should be clear from the above, this terminology is misleading in the sense that ψ̂ is not a once more quantized version of the wave function, but an object which is directly (or via a Fourier ...
Document
... (i) Explain the terms elastic collision and inelastic collision An elastic collision is a collision in which the total kinetic energy of the colliding bodies after collision is equal to their total kinetic energy before collision. Elastic collisions occur only if there is no conversion of kinetic en ...
... (i) Explain the terms elastic collision and inelastic collision An elastic collision is a collision in which the total kinetic energy of the colliding bodies after collision is equal to their total kinetic energy before collision. Elastic collisions occur only if there is no conversion of kinetic en ...
General Chemistry
... hydrogen-bond donor. This electronegative element attracts the electron cloud from around the hydrogen nucleus and, by decentralizing the cloud, leaves the atom with a positive partial charge. Because of the small size of hydrogen relative to other atoms and molecules, the resulting charge, though o ...
... hydrogen-bond donor. This electronegative element attracts the electron cloud from around the hydrogen nucleus and, by decentralizing the cloud, leaves the atom with a positive partial charge. Because of the small size of hydrogen relative to other atoms and molecules, the resulting charge, though o ...
Operators in Quantum Mechanics
... Extensive account of Operators Historic development of quantum mechanics from classical mechanics The Development of Classical Mechanics Experimental Background for Quantum mecahnics Early Development of Quantum mechanics ...
... Extensive account of Operators Historic development of quantum mechanics from classical mechanics The Development of Classical Mechanics Experimental Background for Quantum mecahnics Early Development of Quantum mechanics ...
Band Theory of Solids
... Characteristics of metallic bond: • Metallic solids are malleable and ductile. • They have high electrical and thermal conductivities. • Metallic solids are not soluble in polar and non polar solvents. • These metals have high optical reflection and absorption coefficients. • Due to the symmetrical ...
... Characteristics of metallic bond: • Metallic solids are malleable and ductile. • They have high electrical and thermal conductivities. • Metallic solids are not soluble in polar and non polar solvents. • These metals have high optical reflection and absorption coefficients. • Due to the symmetrical ...
Another version - Scott Aaronson
... Prove #P-completeness for natural average-case approximation problems (like permanents of Gaussians)— thereby yielding hardness for approximate BosonSampling As a first step, understand the distribution of Per(X), X Gaussian Early experimental implementations have been done (Rome, Brisbane, Vienna, ...
... Prove #P-completeness for natural average-case approximation problems (like permanents of Gaussians)— thereby yielding hardness for approximate BosonSampling As a first step, understand the distribution of Per(X), X Gaussian Early experimental implementations have been done (Rome, Brisbane, Vienna, ...
Hydrogen atom
A hydrogen atom is an atom of the chemical element hydrogen. The electrically neutral atom contains a single positively charged proton and a single negatively charged electron bound to the nucleus by the Coulomb force. Atomic hydrogen constitutes about 75% of the elemental (baryonic) mass of the universe.In everyday life on Earth, isolated hydrogen atoms (usually called ""atomic hydrogen"" or, more precisely, ""monatomic hydrogen"") are extremely rare. Instead, hydrogen tends to combine with other atoms in compounds, or with itself to form ordinary (diatomic) hydrogen gas, H2. ""Atomic hydrogen"" and ""hydrogen atom"" in ordinary English use have overlapping, yet distinct, meanings. For example, a water molecule contains two hydrogen atoms, but does not contain atomic hydrogen (which would refer to isolated hydrogen atoms).