Chapter 4 Orbital angular momentum and the hydrogen atom
... which is larger than what is implied by angular momentum conservation. The energy degeneracy for different values of l is a special property of the pure Coulomb interaction. It is lifted in nature by additional interaction terms that lead to the fine structure and hyperfine structure of the spectral ...
... which is larger than what is implied by angular momentum conservation. The energy degeneracy for different values of l is a special property of the pure Coulomb interaction. It is lifted in nature by additional interaction terms that lead to the fine structure and hyperfine structure of the spectral ...
THE WHOLE IS MORE THAN THE SUM OF ITS PARTS
... gravitational forces acting between the planets, and thus needed to solve only one-body problems, treating one planet at a time. The special inverse-square nature of the gravitational force allowed him to obtain his solutions in closed algebraic form, suitable for numbers to be “plugged in” to obtai ...
... gravitational forces acting between the planets, and thus needed to solve only one-body problems, treating one planet at a time. The special inverse-square nature of the gravitational force allowed him to obtain his solutions in closed algebraic form, suitable for numbers to be “plugged in” to obtai ...
introductory quantum theory
... This is the free Schrödinger equation in one spatial dimension. Substituting in our plane wave (2.1) we indeed find that E 2 = p2 /2m. It is clear that there are other equations that might satisfy our requirements (linearity and the correct energy/momentum relation) but this is the simplest. Defini ...
... This is the free Schrödinger equation in one spatial dimension. Substituting in our plane wave (2.1) we indeed find that E 2 = p2 /2m. It is clear that there are other equations that might satisfy our requirements (linearity and the correct energy/momentum relation) but this is the simplest. Defini ...
How close can we get waves to wavefunctions, including potential?
... Δx is the distance between the beads. Since the right-hand side of equation (3) represents mass times acceleration, all terms on the left-hand side are obviously forces. The second term is thus a force proportional to displacement. This can be a spring obeying Hooke's law and K(x) is then the spring ...
... Δx is the distance between the beads. Since the right-hand side of equation (3) represents mass times acceleration, all terms on the left-hand side are obviously forces. The second term is thus a force proportional to displacement. This can be a spring obeying Hooke's law and K(x) is then the spring ...
Physics 171.303: Quantum Mechanics I Fall Semester, 2014 Course
... Overview: This course is the first semester of a two-semester course providing an introduction of quantum mechanics, covering non-commuting observables, angular momentum, two-state systems, time evolution, the wave equation in one dimension, and the simple harmonic oscillator. Prerequisites: Physics ...
... Overview: This course is the first semester of a two-semester course providing an introduction of quantum mechanics, covering non-commuting observables, angular momentum, two-state systems, time evolution, the wave equation in one dimension, and the simple harmonic oscillator. Prerequisites: Physics ...
Electric polarizability of the hydrogen atom
... hydrogen, and it represents a first example of linear response of a system to an external field. Many textbooks (e.g ref.[1]) discuss a classical approach to α assuming that the hydrogen can be approximated by a static charge distribution where the electron density is spherically symmetric and unifo ...
... hydrogen, and it represents a first example of linear response of a system to an external field. Many textbooks (e.g ref.[1]) discuss a classical approach to α assuming that the hydrogen can be approximated by a static charge distribution where the electron density is spherically symmetric and unifo ...
Foundational Questions Institute (FQXi)
... seems to be telling a different story. It is known, for example, that Einstein's equations themselves can be derived as thermodynamic relations. The deep meaning of such results remains a mystery to this day. Our approach will be to push the implications of these results as far as possible as we exp ...
... seems to be telling a different story. It is known, for example, that Einstein's equations themselves can be derived as thermodynamic relations. The deep meaning of such results remains a mystery to this day. Our approach will be to push the implications of these results as far as possible as we exp ...
the problem book
... allowed values of n, and specify how â and ↠act on the stationary states, |ni. Assume that the harmonic oscillator also has a charge q and consider the effects of a constant electric field, E~ = E0 x̂. [6 pt] ...
... allowed values of n, and specify how â and ↠act on the stationary states, |ni. Assume that the harmonic oscillator also has a charge q and consider the effects of a constant electric field, E~ = E0 x̂. [6 pt] ...
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? ...
Quantum mechanics of electrons in strong magnetic field
... To obtain a more concrete idea about the size of the gap between two adjacent Landau levels, we estimate itthe Landau gap. In a typical metal in the field B of the order 10T and taking electron mass me ' 10−27 g, one can estimate the gap roughly as ~Ω = ~eB/me c ' 1.5 ∗ 10−15 erg ' 15K. In a semico ...
... To obtain a more concrete idea about the size of the gap between two adjacent Landau levels, we estimate itthe Landau gap. In a typical metal in the field B of the order 10T and taking electron mass me ' 10−27 g, one can estimate the gap roughly as ~Ω = ~eB/me c ' 1.5 ∗ 10−15 erg ' 15K. In a semico ...
The fallacy of Feynman`s and related arguments on the stability of
... rather than a most probable electron position, momentum, and energy. 7.) The faulty logic is compounded by the fact that the HUP is founded on the definition of the momentum operator given by Eq. (9) and the position operator given by Eq. (10). Thus, the HUP is based on the postulated SE and its ass ...
... rather than a most probable electron position, momentum, and energy. 7.) The faulty logic is compounded by the fact that the HUP is founded on the definition of the momentum operator given by Eq. (9) and the position operator given by Eq. (10). Thus, the HUP is based on the postulated SE and its ass ...
Monte Carlo: A Simple Simulator`s View
... Statistical Mechanics Weight of a particular configuration: ...
... Statistical Mechanics Weight of a particular configuration: ...
Quantum communication: Approaching the quantum limit
... quantum limit of performance. Before describing their strategy in more detail, let us first consider why the problem of verifying the contents of a single box is so non-trivial. Suppose that a logical ‘1’ is represented by a light pulse with a non-zero amplitude, whereas a logical ‘0’ is transmitted ...
... quantum limit of performance. Before describing their strategy in more detail, let us first consider why the problem of verifying the contents of a single box is so non-trivial. Suppose that a logical ‘1’ is represented by a light pulse with a non-zero amplitude, whereas a logical ‘0’ is transmitted ...
Pauli`s exclusion principle in spinor coordinate space
... The Pauli exclusion principle has been an enigmatic element of quantum mechanics from the start. Theoretical developments (1) support the experimentally observed effects, but the explanations have always been considered unintuitive and mathematically intricate. Quantum field theory (2; 3), argues th ...
... The Pauli exclusion principle has been an enigmatic element of quantum mechanics from the start. Theoretical developments (1) support the experimentally observed effects, but the explanations have always been considered unintuitive and mathematically intricate. Quantum field theory (2; 3), argues th ...
Quantum mechanics in more than one
... on |a, bmin $ with L̂+ , we generate a sequence of states with L̂z eigenvalues bmin + !, bmin + 2!, bmin + 3!, · · ·. This series must terminate, and the only possible way for that to happen is for bmax to be equal to bmin + n! with n integer, from which it follows that bmax is either an integer or ...
... on |a, bmin $ with L̂+ , we generate a sequence of states with L̂z eigenvalues bmin + !, bmin + 2!, bmin + 3!, · · ·. This series must terminate, and the only possible way for that to happen is for bmax to be equal to bmin + n! with n integer, from which it follows that bmax is either an integer or ...
The Quantum World The quantum revolution is usually considered
... The letter E on the right side of this equation represents the energy of the quantum state Ψ. However, as Schrödinger soon realized, not all values of E will work. To be more specific, for some special values of E, there will be a solution Ψ to this equation, but for other values of E, there will b ...
... The letter E on the right side of this equation represents the energy of the quantum state Ψ. However, as Schrödinger soon realized, not all values of E will work. To be more specific, for some special values of E, there will be a solution Ψ to this equation, but for other values of E, there will b ...
Observable and hidden singular features of large fluctuations
... can be found from the condition that the energy of the Hamiltonian motion E = 0. The paths infinitesimally close toMPEP ([C(I) I ---, 0) and lyingon the opposite sides of it approach asymptotically the eigenvectors ±qO) as t ~ ~ and then go away from the saddle point. The corresponding limiting path ...
... can be found from the condition that the energy of the Hamiltonian motion E = 0. The paths infinitesimally close toMPEP ([C(I) I ---, 0) and lyingon the opposite sides of it approach asymptotically the eigenvectors ±qO) as t ~ ~ and then go away from the saddle point. The corresponding limiting path ...