PCHEM TERMS - Quantum Mechanics

black body object

an object capable of emitting and absorbing all wavelengths of radiation without favoring any wavelength. From Atkins, Physical Chemistry 11th Ed, page 245, entered by Darren Williams.

photoelectric effect

The ejection of electrons when light (with energy above the work function) strikes a surface. This supports the view that electromagnetic radiation consists of particles (photons). From Atkins, Physical Chemistry 11th Ed, page 245, entered/ edited by Darren Williams.

Diffraction

the interference caused by an object in the path of waves and occurs when the dimensions of the object are comparable to the wavelength of the radiation.

From Atkins, Physical Chemistry 11th Ed, page 238, entered by Taylor Shelley.

Wave-Particle Duality

The recognition that some experiments support the particle nature of light and matter while other experiments support the wave nature of light and matter.

From Atkins, Physical Chemistry 11th Ed, page 242, entered by Taylor Shelley - edited by Dr. Williams

Wavefunction

a mathematical function that contains all the dynamical information about a system.

From Atkins, Physical Chemistry 11th Ed, page 250, entered by Taylor Shelley.

Uncertainty Principle

restricts the precision with which complementary observables may be specified and measured simultaneously.

From Atkins, Physical Chemistry 11th Ed, page 257, entered by Taylor Shelley.

Correspondence Principle

states that the quantum mechanical result with high quantum numbers should agree with the predictions of classical mechanics.

From Atkins, Physical Chemistry 11th Ed, page 265, entered by Taylor Shelley.

speed of light

symbol c

2.997 924 58* 10^8 ms^-1

Atkins, Physical Chemistry 11th Ed, on the Fundamental Constants table, entered by Megan Mann

Planck's constant

symbol h

6.626 069 57x10^−34 Js

Atkins, Physical Chemistry 11th Ed, on the Fundamental Constants table, entered by Megan Mann

wavelength

Horizontal distance between the crests or between the troughs of two adjacent waves

symbol λ

By Megan Mann

frequency

the number of complete wavelengths that pass a point in a given time

symbol v

By Megan Mann

Zero-Point Energy

The lowest, irremovable energy that a particle can possess. Zero-point energy.

From Atkins, Physical Chemistry 11th Ed, page 265, entered by Donovan Hastings.

kinetic energy

The energy the body possesses as a result of its motion.

E = (1/2)(m)(v^2)

Atkins', physical chemistry 11th edition, pg. 35

entered by Marrisa Martinez

potential energy

The energy a body possesses as a result of its position. In the absence of losses, the potential energy of a stationary particle is equal to the work that had to be done on the body to bring it to its current location.

Atkins', physical Chemistry 11th edition, pg.35

entered by Marrisa Martinez

quantum mechanics

The theory that wave mechanics can describe the discrete energy levels that match spectroscopic observations. These observations couldn't be explained by the classical mechanics developed by Newton

Atkins', Physical Chemistry 11th edition, pg 237

Makenzie Kuehn - edited by Dr. Williams

wavenumber

The reciprocal of the wavelength and can be interpreted as the number of wavelengths in a given distance. Usually represented by ṽ the equations associated with it are:

ṽ=1/λ or ṽ=v/c

Atkins', Physical Chemistry 11th edition, pg 238

Makenzie Kuehn

electromagnetic radiation

form of energy that is produced by oscillating electric and magnetic disturbances, or by the movement of electrically charged particles traveling through a vacuum or matter.

Libretexts. "Electromagnetic Radiation." Chemistry LibreTexts, Libretexts, 5 June 2019. entered by Marrisa Martinez

energy quantization

The limitation of energies to discrete values

Atkins', Physical Chemistry 11th edition, pg. 239

entered by Marrisa Martinez - edited by Dr. Williams

energy density E(T)

the total energy inside the container divided by its volume

Atkins', Physical Chemistry 11th edition, pg 238

Makenzie Kuehn

Bohr frequency condition

ΔE=hv is the relationship between radiation absorbed/emitted (∆E) and frequency (v)

Atkins', Physical Chemistry 11th edition, pg 241

Makenzie Kuehn - edited by Dr. Williams

spectroscopy

direct evidence for the quantization of energy; the detection and analysis of the electromagnetic radiation absorbed, emitted, or scattered by a substance.

Atkins', Physical Chemistry 11th edition, pg. 241

entered by Marrisa Martinez

spectrum

the record of the variation of the intensity of the electromagnetic radiation with frequency (v), wavelength (λ), or wavenumber (ṽ=v/c)

Atkins', Physical Chemistry 11th edition, pg 241

Makenzie Kuehn

photoelectric effect

the ejection of electrons from metals when they are exposed to ultraviolet radiation; experimental characteristics:

1. no electrons are rejected unless frequency exceeds a threshold value of the metal

2. kinetic energy of the ejected electrons increases linearly with the frequency, but is independent of the intensity of the radiation.

3. electrons are rejected immediately if the frequency is above threshold value

Atkins', physical chemistry 11th edition, pg. 243. entered by Marrisa Martinez

degeneracy

a count of different wave functions that have the same energy. Atkins', Physical Chemistry 11th edition, pg 268

Patricia Hernandez - edited by Dr. Williams

boundary conditions

conditions a wavefunction must satisfy in order to be acceptable. Atkins', Physical Chemistry 11th edition, pg 263

Patricia Hernandez

Spectroscopic transition

a change of quantum state that absorbs, emits, or scatters a photon of light

Atkins', Physical Chemistry 11th edition, pg 241. Vivian Moreno - edited by Dr. Williams

Hamiltonian Operator

The operator corresponding to the total energy of the system, the sum of the kinetic and potential energies.

Atkins', Physical Chemistry 11th edition, pg 260, entered by Ryan Phillips.

Cyclic Boundary Conditions

If a wavefunction satisfies this condition, quantization occurs. The energy and angular momentum for a particle rotating in a two or three-dimensions are quantized.

Atkins', Physical Chemistry 11th edition, pg 290, entered by Ryan Phillips.

Born interpretation of wave functions

The most commonly accepted interpretation of the wavefunction that the square of the modulus is proportional to the probability density (probability per unit volume) that the electron is in the volume dτ located at ri.

Libretexts. "3.4: Wavefunctions Have a Probabilistic Interpretation." Chemistry LibreTexts, Libretexts, 14 July 2019, chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Map:_Physical_Chemistry_(McQuarrie_and_Simon)/03._The_Schrodinger_Equation_and_a_Particle_In_a_Box/3.4:_Wavefunctions_Have_a_Probabilistic_Interpretation.

Ever Guzman

probability distribution

the square of the wave function gives the likelihood that a particle will be found in a particular space. from Postulate 1, pchem notes, entered by Dr. Williams (Original mathematical definition was deleted because it was not from a pchem source.)

kronecker delta

a function of two variables that is 1 when the variables have the same value and is 0 when they have different values.

Kronecker Delta. (n.d.). Retrieved from https://www.merriam-webster.com/dictionary/Kronecker delta

Ever guzman

Blackbody radiation

The light emitted by all objects at temperatures above absolute zero.

Spectroscopy in one Dimension by D.Willians, v.Jackson, pg 3. Vivian Moreno - edited by Dr. Williams

N-fold Degeneracy

Energy levels are N-fold degenerate if N wavefunctions correspond to the same energy (where N is the number of corresponding wavefunctions).

Atkins', Physical Chemistry 11th edition, pg 271, entered by Ryan Phillips.

First Derivative

Denoted by f'. df/dx = the limit as δx approaches zero of [f(x+δx)-f(x)]/δx

This equation can be interpreted as the slope of the tangent to the graph of f(x) at a given value of x.

Atkins', Physical Chemistry 11th edition, pg 22, entered by Ryan Phillips.

Second Derivative

Denoted by simply f", or rather d²f/dx² = the limit as δx approaches zero of [f'(x+δx)-f'(x)]/δx

The second derivative of a function indicates the sharpness of its curve. The second derivative is equal to zero at a point of inflection, where the first derivative changes sign.

Atkins', Physical Chemistry 11th edition, pg 22, entered by Ryan Phillips.

Complex Conjugate

Formed by replacing i with -i. Complex numbers have the general form z=x+iy. The real number x, is the real part of z, while y is the imaginary part of z.

Atkins', Physical Chemistry 11th edition, pg247, entered by Aurelia Holifield

Standing Wave Diagram

This shows where the nodes and lobes are located on a simple wave function. I found this information in chapter one of the notes uploaded by Dr. Williams. Aurelia Holifield

lobe

where the oscillation of the wave occurs. This comes from the notes for lecture. Aurelia Holifield

node

Part of the wave where no movement occurs. A "fixed place". From the notes for lecture. Aurelia Holifield

Eigenvalue Equations

is an equation with the form of (operator)(function)=(Constant factor)x(same function). The action of the operator on the function generates the same function, multiplied by a constant. From Atkins, Physical Chemistry 11th ED, page 251, Entered by Ryan Goldstein.

Observables

The measurable properties of the system, such as linear momentum, position, and energy.

From Atkins, Physical Chemistry 11th ED, page 252, Entered by Ryan Goldstein - edited by Dr. Williams

Hermitian operator

If the relation is true the value is a Hermitian

∫Ψi* ΩΨj dτ=∫Ψj* ΩΨi dτ Hermitian operators have real eigenvalues and orthogonal eigenfuctions. From Atkins, Physical Chemistry 11th ED, page 253 and 254, Entered by Ryan Goldstein - edited by Dr. Williams

work function

The energy required to remove an electron from a metal to infinity.

Atkins, Peter and Julio de Paula. Physical Chemistry. 10 ed., W. H. Freeman, 2014. (Pg 288)

Entered by Brianna Ecolango

Complementary observables

Observables for which the corresponding operators do not commute From Atkins Physical Chemistry 11th Ed., page 260, entered by Cailee Auck

Normalized Wavefunction

The integral over all space of its square modulus is equal to 1 From Atikins Physical Chemistry 11th Ed., page 250 Entered by Cailee Auck

de Broglie Relation

Any particle traveling with linear momentum corresponds to a wavelength From Atkins Physical Chemistry 11th Ed. Entered by Cailee Auck

Ultraviolet catastrophe

The concentration of emitted radiation at short wavelengths, an unavoidable consequence of classical physics.

From Atkins Physical Chemistry 11th Ed., page 239, entered by Cailee Auck - edited by Dr. Williams

Quantum number

An integer (in some cases a half-integer) that labels the state of the system From Atkins Physical Chemistry 11th Ed., page 263. Entered by Cailee Auck

Tunneling

The ability of a particle to penetrate into, and possibly pass through, a classically forbidden region.

From Atkins Physical Chemistry 11th Ed., page 268. Entered by Cailee Auck

Orthonormal

Functions that are both normalized and mutually orthogonal, meaning that the integral over all space of Ψi*Ψj = δi,j , which is 1 when i=j and 0 when i<>j.

Atkins, Peter, et al. Atkins' Physical Chemistry. 11 ed., Oxford University Press, 2018. (Pg 254) Entered by Brianna Ecolango - edited by Dr. Williams

Wavepacket

A sharply localized wavefunction which can be created by forming a linear combination of wavefunctions that correspond to many different linear momenta.

Atkins, Peter, et al. Atkins' Physical Chemistry. 11 ed., Oxford University Press, 2018. (Pg 258)

Entered by Brianna Ecolango

Electronvolt (eV)

The energies of photoelectrons, the work function, and other quantities are often expressed in this unit. 1 eV is defined as the kinetic energy acquired when an electron is accelerated from rest through a 1 Volt potential difference.

Atkins, Peter, et al. Atkins' Physical Chemistry. 11 ed., Oxford University Press, 2018. (Pg 243)

Entered by Breanna Nelson - edited by Dr. Williams

Valid wave functions

Must be continuous, single valued, finite, continuous slope, and satisfy the boundry conditions. Lecture notes titled The Scrodinger Equation and the 1DPB Wave Function slide 2 Entered by Aurelia Holifield

position operator

x as in =

Lecture notes titles Supplemental Material the Quantum Mechanical Postulates Entered by Aurelia Holifield - edited by Dr. Williams

potential energy operator

V(x) Lecture notes titles Supplemental Material the Quantum Mechanical Postulates Entered by Aurelia Holifield

spontaneous emission

a molecule or atom makes a transition to a lower state without being driven by the presence of radiation. The precise time of emission cannot be predicted for a particular particle.

Atkins', Physical Chemistry 11th edition, pg. 420

entered by Marrisa Martinez - edited by Dr. Williams

stimulated emission

a photon causes a molecule to transition from an upper state to a lower state which generates a second photon in-phase and with the same frequency as the incident photon.

Atkins', Physical Chemistry 11th edition, pg. 420

entered by Marrisa Martinez - edited by Dr. Williams

Hot Bands

Spectroscopic transitions by atoms, ions, or molecules originating from an exited state.

DW powerpoint in class. Entered by Kaylyn Keith - edited by Dr. Williams

Transition Equation

Computes the energy differences between quantum states showing where a spectroscopic peak will appear on the horizontal axis in a spectrum.

DW powerpoint in class. Entered by Kaylyn Keith - edited by Dr. Williams

Overtones

Spectroscopic transitions that skip multiple quantum levels. Or, transitions between non-adjacent quantum states.

DW powerpoint in class. Entered by Kaylyn Keith - edited by Dr. Williams

Heisenberg uncertainty principle

The principle states that it is impossible to detect the linear and momentum and position of the particle at the same time.

Atkins, Peter, et al. Atkins' Physical Chemistry. 11 ed., Oxford University Press, 2018. (Pg 257). Entered by Phillip Paik

Fundamental Transition

The first allowed transition from the ground state to the first allowed excited state. (n=1 to n=2 in the 1DPB system)

Transition Dipole Moments and Transition Equations powerpoint from lecture. Entered by Kyler Kelley - edited by Dr. Williams

Selection Rules

The set of allowed transitions for a particular spectroscopic experiment, for example the allowed transitions for absorbance in a particle in a 1D box are ∆n = {1, 3, 5, ...}

L05 Notes, entered by Dr. Williams

Wien's law

At each temperature, T, there is a wavelength, λmax, at which the intensity of the radiation is a maximum, with T and λmax related by an empirical formula.

Atkins, Peter, et al. Atkins' Physical Chemistry. 11 ed., Oxford University Press, 2018. (Pg 238) Entered by Breanna Nelson