Physical Sciences and Mathematics Commons^™

Many-Particle Systems, 1, David Peak

Many Particles

Wavefunctions for more than one particle: Different kinds of particles

Introductory examples of quantum mechanical wavefunction calculations involve a single particle moving about in a “magic” potential energy—e.g., a particle trapped inside a square well or an electron in a hydrogen atom. But, potential energy arises from interaction, so these situations must inevitably include more than one particle. Even the simplest atom—hydrogen— consists of two particles: the electron and the proton. So, how should the Schrödinger Equation be generalized to account for multiple particles?

Many-Particle Systems, 8, David Peak

Many Particles

The classical picture of how electrons migrate through a resistor driven by an applied potential difference draws an analogy with a kind of pinball machine. In a pinball machine, gravity accelerates the pinball down the table, but the ball’s progress is impeded by collisions with bumpers, as depicted to the right. (θ is the angle the table makes with the horizontal direction.) When averaged over many collisions the ball’s average equation of motion is ma = mg sinθ − mv/τ , where a and v are directed down the table, and τ is the average time between collisions. If the …

Problem Set #11, David Peak

Problems

In problems 1-3 compare the average number density ρ with the quantum number density

Problem Set #10, David Peak

Problems

Blackbody

Problem Set #4, David Peak

Problems

Some 1D infinite well stuff

Problem Set #12, David Peak

Problems

Solid stuff

Problem Set #6, David Peak

Problems

3D, 1-particle systems

Problem Set #3, David Peak

Problems

Comparing classical electromagnetic waves with photon probability waves.

Problem 1 refers to: A standing electric field wave (one with lots of photons) in a quantum wire stretching between x = 0 and x = L is described by E(x,t)=E_maxsin(3πx/L)cos(3πct/L). Let L = 900 nm.

Problem Set #1, David Peak

Problems

A little E&M practice

Problems 1-2 refer to: The electric field in a laser beam is given by E( x,t) = (1000V/m)sin[(πx10⁷rad/m) x + (3πx10¹⁵rad/s)t].

Problem Set #7, David Peak

Problems

Atom stuff

Problem Set #8, David Peak

Problems

A bit of stat mech

Problems 1-3 refer to: N identical, noninteracting, and distinguishable spin-1/2 particles (i.e., their separation is much greater than their de Broglie wavelength) are placed in an external magnetic field. Assume the ground state energy of one such particle is 0 and the excited state energy is ε , and the system is in thermal equilibrium at temperature T.

Problem Set #5, David Peak

Problems

Expectations & 1D finite wells

Problem Set #2, David Peak

Problems

A little energy and momentum practice (and units)

Problems 1-2 deal with “rest” energy and relativity.

Problem Set #9, David Peak

Problems

Another bit of stat mech

Problems 1-3 refer to: N identical, noninteracting, and distinguishable quantum harmonic oscillators (i.e., their separation is much greater than their de Broglie wavelength) are in thermal equilibrium at temperature T. The energy of each oscillator can be expressed as ε_n = nε , where ε is the level spacing and n = 0, 1, 2, … .

Schrödinger, 2, David Peak

Schrodinger

The finite square well

The infinite square well potential energy rigorously restricts the associated wavefunction to an exact region of space: it is infinitely “hard.” Potential energies encountered in more realistic physical scenarios are “softer” in that they permit wavefunctions to spread throughout less well-defined regions. An important toy example of the latter is the finite square well. In this problem, the potential energy function is U(x) = 0, if 0 < x < L, and U₀ otherwise.

Schrödinger, 3, David Peak

Schrodinger

The 3D infinite square well: quantum dots, wells, and wires

In the preceding discussion of the Schrödinger Equation the particle of interest was assumed to be “moving in the x -direction.” Of course, it is not possible for a particle to be moving in one spatial direction only. If that were true, according to the HUP it could be anywhere in the y - and z -directions and therefore be undetectable with finite volume detectors. Now, we consider the more realistic case of motion in all three spatial directions. For this purpose, we start with the 3D infinite square well. …

Schrödinger, 1, David Peak

Schrodinger

The Schrödinger equation: the quantum description of one massive, slow-moving particle

To establish a probability wave equation for one photon, it was useful to note that probability density and electromagnetic energy density were proportional. The governing equation for EM radiation fields is the Maxwell wave equation, which is also the governing equation for photon probability wave functions. Converting from EM radiation to photon information is made plausible by identifying energy and momentum operators with time- and space-derivatives, respectively. Thus, the Maxwell wave equation can be interpreted as being equivalent to the energy-momentum relation for photons. Though we don’t have a …

Schrödinger, 5, David Peak

Schrodinger

Transitions

Schrödinger, 4, David Peak

Schrodinger

The sanitized hydrogen atom: separating the variables

Separation of variables in the Schrödinger Equation for the hydrogen problem requires expressing Ψ as a product, Ψ(r,θ,φ,t) = R(r)Θ(θ )Φ(φ)T(t) , substituting into the partial differential equation [(5) in Sc3], and then dividing by Ψ. As in the square well problems, the separation constant for the t part of the separation is the particle’s eigen-energy, E.

Physics 2710: Introductory Modern Physics, David Peak

Syllabus

No abstract provided.

History Of Computing, George K. Thiruvathukal, David B. Dennis

Computer Science: Faculty Publications and Other Works

The social and organizational history of humanity is intricately entangled with the history of technology in general and the technology of information in particular. Advances in this area have often been closely involved in social and political transformations. While the contemporary period is often referred to by such names as the Computing and Information Age, this is the culmination of a series of historical transformations that have been centuries in the making. This course will provide a venue for students to learn about history through the evolution of number systems and arithmetic, calculating and computing machines, and advanced communication technology …

Microhh 1.0: A Computational Fluid Dynamics Code For Direct Numerical Simulation And Large-Eddy Simulation Of Atmospheric Boundary Layer Flows, Chiel C. Van Heerwaarden, Bart J.H. Van Stratum, Thijs Heus, Jeremy A. Gibbs, Evgeni Fedorovich, Juan Pedro Mellado

Physics Faculty Publications

© 2017 Author(s). This paper describes MicroHH 1.0, a new and open-source (www.microhh.org) computational fluid dynamics code for the simulation of turbulent flows in the atmosphere. It is primarily made for direct numerical simulation but also supports large-eddy simulation (LES). The paper covers the description of the governing equations, their numerical implementation, and the parameterizations included in the code. Furthermore, the paper presents the validation of the dynamical core in the form of convergence and conservation tests, and comparison of simulations of channel flows and slope flows against well-established test cases. The full numerical model, including the associated parameterizations for …

Sea Level Rise May Increase Extinction Risk Of A Saltmarsh Ontogenetic Habitat Specialist, David S. Johnson, Bethany L. Williams

VIMS Articles

Specialist species are more vulnerable to environmental change than generalist species. For species with ontogenetic niche shifts, specialization may occur at a particular life stage making those stages more susceptible to environmental change. In the salt marshes in the northeast U.S., accelerated sea level rise is shifting vegetation patterns from flood-intolerant species such as Spartina patens to the flood-tolerant Spartina alterniflora. We tested the potential impact of this change on the coffee bean snail, Melampus bidentatus, a numerically dominant benthic invertebrate with an ontogenetic niche shift. From a survey of eight marshes throughout the northeast U.S., small snails …

Rating By Ranking: An Improved Scale For Judgement-Based Labels, Jack O'Neill, Sarah Jane Delany, Brian Mac Namee

Conference papers

Labels representing value judgements are commonly elicited using an interval scale of absolute values. Data collected in such a manner is not always reliable. Psychologists have long recognized a number of biases to which many human raters are prone, and which result in disagreement among raters as to the true gold standard rating of any particular object. We hypothesize that the issues arising from rater bias may be mitigated by treating the data received as an ordered set of preferences rather than a collection of absolute values. We experiment on real-world and artificially generated data, finding that treating label ratings …

Analysis Of The Impact Of Marine Mrv Program And Market Emission Reduction Measures On China's Shipping Industry, Qiwen Wang

Maritime Safety & Environment Management Dissertations (Dalian)

No abstract provided.

Research On Ship Emission Reduction In Guangzhou Port Under The Policy Of Domestic Emission Control Areas (Decas) In China, Xiaoyu Li

Maritime Safety & Environment Management Dissertations (Dalian)

No abstract provided.

The Future Is Coming : Research On Maritime Communication Technology For Realization Of Intelligent Ship And Its Impacts On Future Maritime Management, Jiacheng Ke

Maritime Safety & Environment Management Dissertations (Dalian)

No abstract provided.

Research On Optimal Allocation Of Oil Spill Contingency Resources Base On Oil Spill Risk Assessment In Taizhou Port, Liangyu Wang

Maritime Safety & Environment Management Dissertations (Dalian)

No abstract provided.

Research On Improving Navigation Safety Based On Big Data And Cloud Computing Technology For Qiongzhou Strait, Rui Wang

Maritime Safety & Environment Management Dissertations (Dalian)

No abstract provided.

Analyses And Predictions Of Traffic Flows And Incidents In Mirs Bay Water, Chao Jiang

Maritime Safety & Environment Management Dissertations (Dalian)

No abstract provided.