Columbia University in the City of New York · Courses
APPH E
38 courses with the subject APPH E, each shown exactly as we captured it from the college's catalog, with every element we hold. Where the wording looks broken, that is our reading of the catalog, not the college's text.
APPH E3100INTRO TO QUANTUM MECHANICS3.00
Prerequisites: (PHYS UN1403) or PHYS W1403; APMA E3101; or equivalent, and differential and integral calculus. Corequisites: APMA E3101 Basic concepts and assumptions of quantum mechanics, Schrodinger's equation, solutions for one-dimensional problems including square wells, barriers and the harmonic oscillator, introduction to the hydrogen atom, atomic physics and X-rays, electron spin
Prerequisites: (PHYS UN1402) and (MATH UN2030) or MATH V2030 AND PHYS C1402; or equivalent. Basic non-Euclidean coordinate systems, Newtonian Mechanics, oscillations, Greens functions, Newtonian graviation, Lagrangian mechanics, central force motion, two-body collisions, noninertial reference frames, rigid body dynamics. Applications, including GPS and feedback control systems, are emphasized throughout
Prerequisites: APMA E3102 Corequisites: APMA E3102 Vector analysis, electrostatic fields, Laplaces equation, multipole expansions, electric fields in matter: dielectrics, magnetostatic fields, magnetic materials, and superconductors. Applications of electromagnetism to devices and research areas in applied physics
Prerequisites: Written permission from instructor and approval from adviser. This course may be repeated for credit, but no more than 6 points of this course may be counted toward the satisfaction of the B.S. degree requirements. Candidates for the B.S. degree may conduct an investigation in applied physics or carry out a special project under the supervision of the staff. Credit for the course is contingent upon the submission of an acceptable thesis or final report
Subject
APPH E
Credits (min)
0
Credits (max)
4
Credit unit
points
Type
course
Repeatable
may be repeated for credit, but no more than 6 points of this course may be counted toward the satisfaction of the B.
Prerequisites: APMA E2000 AND MATH V1202 AND MATH V2030 AND PHYS W1403; or equivalents. Introductory course is for individuals with an interest in medical physics and other branches of radiation science. Topics include basic concepts, nuclear models, semi-empirical mass formula, interaction of radiation with matter, nuclear detectors, nuclear structure and instability, radioactive decay process and radiation, particle accelerators, and fission and fusion processes and technologies
Prerequisites: Recommended but not required: APPH E3100 and APPH E3300 or their equivalents. Optical resonators, interaction of radiation and atomic systems, theory of laser oscillation, specific laser systems, rate processes, modulation, detection, harmonic generation, and applications
Prerequisites: APPH E3300 AND PHYS W3008 Advanced senior-level/MS/PhD course covering interaction of laser light with matter in both classical and quantum domains. First half introduces microscopic origin of optical nonlinearities through formal derivation of nonlinear susceptibilities, emphasis on second- and third-order optical processes. Topics include Maxwell's wave equation, and nonlinear optical processes such as second-harmonic, difference frequency generation, four-wave mixing, and self-phase modulation, including various applications of processes such as frequency conversion, and optical parametric amplifiers and oscillators. Second half describes two-level atomic systems and quantization of electromagnetic field. Descriptions of coherent, Fock, and squeezed states of light discussed and techniques to generate such states outlined
Prerequisites: General physics PHYS C1401x, C1402y, C1403x, C1601x, and C1602y, freshman mathematics including ordinary differential equations MATH V1201 and MATH V1202, MATH E1210. Familiarity in thermodynamics, electromagnetism, quantum mechanics, solid-state
Lect: 3. An introduction to the physical behavior of fluids for science and engineering students. Derivation of basic equations of fluid dynamics: conservation of mass, momentum, and energy. Dimensional analysis. Vorticity. Laminar boundary layers. Potential flow. Effects of compressibility, stratification, and rotation. Waves on a free surface; shallow water equations. Turbulence. Fall 2026: APPH E4200 Course Number Section/Call Number Times/Location Instructor Points Enrollment APPH 4200 001/14168 Th 4:10pm - 6:40pm 313 Pupin Laboratories Lorenzo Polvani 3.00 30/35
Prerequisites: (APMA E3101) and (APMA E3102) and (APPH E4200) APMA E3101 AND APMA E3102 AND APPH E4200; or equivalents or instructor's permission. Fundamental concepts in the dynamics of rotating, stratified flows. Geostrophic and hydrostatic balances, potential vorticity, f and beta plane approximations, gravity and Rossby waves, geostrophic adjustment and quasigeostrophy, baroclinic and barotropic instabilities, Sverdrup balance, boundary currents, Ekman layers
Prerequisites: APPH E3300 Overview of properties and interactions of static electric and magnetic fields. Study of phenomena of time dependent electric and magnetic fields including induction, waves, and radiation as well as special relativity. Applications are emphasized
x An x following the course number means that the course meets in the fall semester. J The courses that are often taken, or in some cases need to be taken, i the junior year are denoted with a “J.” y A y following the course number means that the course meets in the spring semester. Earth and Atmospheric Sciences The earth sciences provide a wide range of problems of interest to physicists and mathematicians ranging from the dynamics of Earth’s climate to earthquake physics to dynamics of Earth’s deep interior. The Lamont-Doherty Earth Observatory, which is part of Columbia University, provides enormous resources for students interested in this area. Atmosphere, Oceans, and Climate APAM E3109 EESC GU4008 Introduction to Atmospheric Science
Prerequisites: (APPH E4010) APPH E4010; or equivalent. Corequisites: APPH E4010 Interface between clinical practice and quantitative radiation biology. Microdosimetry, dose-rate effects and biological effectiveness thereof; radiation biology data, radiation action at the cellular and tissue level; radiation effects on human populations, carcinogenesis, genetic effects; radiation protection; tumor control, normal-tissue complication probabilities; treatment plan optimization
Prerequisites: (APPH E4600) APPH E4600 OR APPH E6380 Corequisites: APPH E4600 Fundamental principles and objectives of health physics (radiation protection), the quantities of radiation dosimetry (the absorbed dose, equivalent dose, and effective dose) used to evaluate human radiation risks, elementary shielding calculations and protection measures for clinical environments, characterization and proper use of health physics instrumentation, and regulatory and administrative requirements of health physics programs in general and as applied to clinical activities
Required for all graduate students in the Medical Physics Program. Practicing professionals and faculty in the field present selected topics in medical physics
Prerequisites: (APPH E4010) or APPH E4010 OR APPH E4500; or equivalent. Corequisites: APPH E4010 Basic radiation physics: radioactive decay, radiation producing devices, characteristics of the different types of radiation (photons, charged and uncharged particles) and mechanisms of their interactions with materials. Essentials of the determination, by measurement and calculation, of absorbed doses from ionizing radiation sources used in medical physics (clinical) situations and for health physics purposes
Prerequisites: (APPH E4010) or APPH E4010 Corequisites: APPH E4010 Lab fee: $50. Theory and use of alpha, beta, gamma, and X-ray detectors and associated electronics for counting, energy spectroscopy, and dosimetry; radiation safety; counting statistics and error propagation; mechanisms of radiation emission and interaction. (Topic coverage may be revised.)
Required for, and can be taken only by, all applied physics majors and minors in the junior year. Discussion of specific and self-contained problems in areas such as applied electrodynamics, physics of solids, and plasma physics. Topics change yearly
Required for, and can be taken only by, all applied physics majors in the senior year. Discussion of specific and self-contained problems in areas such as applied electrodynamics, physics of solids, and plasma physics. Formal presentation of a term paper required. Topics change yearly
Prerequisites: Instructor's permission. May be repeated for credit. Topics and instructors change from year to year. For advanced undergraduate students and graduate students in engineering, physical sciences, and other fields
Prerequisites: (APPH E3100) APPH E3100; or the equivalent. Knowledge of statistical physics on the level of MSAE E3111 or PHYS GU4023 strongly recommended. Crystal structure, reciprocal lattices, classification of solids, lattice dynamics, anharmonic effects in crystals, classical electron models of metals, electron band structure, and low-dimensional electron structures
Prerequisites: (APPH E4300) APPH E4300 Debye screening. Motion of charged particles in space- and time-varying electromagnetic fields. Two-fluid description of plasmas. Linear electrostatic and electromagnetic waves in unmagnetized and magnetized plasmas. The magnetohydrodynamic (MHD) model, including MHD equilibrium, stability, and MHD waves in simple geometries
Prerequisites: (APPH E6101) APPH E6101 Magnetic coordinates. Equilibrium, stability, and transport of torodial plasmas. Ballooning and tearing instabilities. Kinetic theory, including Vlasov equation, Fokker-Planck equation, Landau damping, kinetic transport theory. Drift instabilities
Prerequisites: (APPH E4010) APPH E4010; or equivalent. Introduction to the instrumentation and physics used in clinical nuclear medicine and PET with an emphasis on detector systems, tomography and quality control. Problem sets, papers and term project
Prerequisites: APPH E6335; Grade of B+ or better in APPH E6335 and instructor's permission. Students spend two to four days per week studying the clinical aspects of radiation therapy physics. Projects on the application of medical physics in cancer therapy within a hospital environment are assigned; each entails one or two weeks of work and requires a laboratory report. Two areas are emphasized: 1. computer-assisted treatment planning (design of typical treatment plans for various treatment sites including prostate, breast, head and neck, lung, brain, esophagus, and cervix) and 2. clinical dosimetry and calibrations (radiation measurements for both photon and electron beams, as well as daily, monthly, and part of annual QA)
Prerequisites: (APPH E4600) APPH E4600; APPH E4330 recommended. Review of X-ray production and fundamentals of nuclear physics and radioactivity. Detailed analysis of radiation absorption and interactions in biological materials as specifically related to radiation therapy and radiation therapy dosimetry. Surveys of use of teletherapy isotopes and X-ray generators in radiation therapy plus the clinical use of interstitial and intracavitary isotopes. Principles of radiation therapy treatment planning and isodose calculations. Problem sets taken from actual clinical examples are assigned
Prerequisites: (APPH E6335) APPH E6335 Advanced technology applications in radiation therapy physics, including intensity modulated, image guided, stereotactic, and hypofractionated radiation therapy. Emphasis on advanced technological, engineering, clinical, and quality assurance issues associated with high technology radiation therapy and the special role of the medical physicist in the safe clinical application of these tools
Prerequisites: APPH6330; Grade of B+ or better in APPH E6330 and instructor's permission. Practical applications of diagnostic radiology for various measurements and equipment assessments. Instruction and supervised practice in radiation safety procedures, image quality assessments, regulatory compliance, radiation dose evaluations and calibration of equipment. Students participate in clinical QC of the following imaging equipment: radiologic units (mobile and fixed), fluoroscopy units (mobile and fixed), angiography units, mammography units, CT scanners, MRI units and ultrasound units. The objective is familiarization in routine operation of test instrumentation and QC measurements utilized in diagnostic medical physics. Students are required to submit QC forms with data on three different types of radiology imaging equipment
Prerequisites: APPH E6319; Grade of B+ or better in APPH E6319 and instructor's permission. Practical applications of nuclear medicine theory and application for processing and analysis of clinical images and radiation safety and quality assurance programs. Topics may include tomography, instrumentation, and functional imaging. Reports
Prerequisites: APPH E4500; Grade of B+ or better in APPH E4500 and instructor's permission. Corequisites: APPH E4500 Radiation protection practices and procedures for clinical and biomedical research environments. Includes design, radiation safety surveys of diagnostic and therapeutic machine source facilities, the design and radiation protection protocols for facilities using unsealed sources of radioactivity – nuclear medicine suites and sealed sources – brachytherapy suites. Also includes radiation protection procedures for biomedical research facilities and the administration of programs for compliance to professional health physics standards and federal and state regulatory requirements for the possession and use of radioactive materials and machine sources of ionizing and non ionizing radiations in clinical situations. Individual topics are decided by the student and the collaborating Clinical Radiation Safety Officer
Plasma and Fusion Colloquium: All plasma and fusion graduate students are strongly encouraged to attend the department seminar as long as they are in residence. Interested undergraduates are also welcome. No degree credit is granted
