Key Terms

Key Terms

anti-symmetric function

odd function

Born interpretation

states that the square of a wave function is the probability density

complex function

function containing both real and imaginary parts

Copenhagen interpretation

states that when an observer is not looking or when a measurement is not being made, the particle has many values of measurable quantities, such as position

correspondence principle

in the limit of large energies, the predictions of quantum mechanics agree with the predictions of classical mechanics

energy levels

states of definite energy, often represented by horizontal lines in an energy “ladder” diagram

energy quantum number

index that labels the allowed energy states

energy-time uncertainty principle

energy-time relation for uncertainties in the simultaneous measurements of the energy of a quantum state and of its lifetime

even function

in one dimension, a function symmetric with the origin of the coordinate system

expectation value

average value of the physical quantity assuming a large number of particles with the same wave function

field emission

electron emission from conductor surfaces when a strong external electric field is applied in normal direction to conductor’s surface

ground state energy

lowest energy state in the energy spectrum

Heisenberg’s uncertainty principle

places limits on what can be known from a simultaneous measurements of position and momentum; states that if the uncertainty on position is small then the uncertainty on momentum is large, and vice versa

infinite square well

potential function that is zero in a fixed range and infinitely beyond this range

momentum operator

operator that corresponds to the momentum of a particle

nanotechnology

technology that is based on manipulation of nanostructures such as molecules or individual atoms to produce nano-devices such as integrated circuits

normalization condition

requires that the probability density integrated over the entire physical space results in the number one

odd function

in one dimension, a function antisymmetric with the origin of the coordinate system

position operator

operator that corresponds to the position of a particle

potential barrier

potential function that rises and falls with increasing values of position

principal quantum number

energy quantum number

probability density

square of the particle’s wave function

quantum dot

small region of a semiconductor nanocrystal embedded in another semiconductor nanocrystal, acting as a potential well for electrons

quantum tunneling

phenomenon where particles penetrate through a potential energy barrier with a height greater than the total energy of the particles

resonant tunneling

tunneling of electrons through a finite-height potential well that occurs only when electron energies match an energy level in the well, occurs in quantum dots

resonant-tunneling diode

quantum dot with an applied voltage bias across it

scanning tunneling microscope (STM)

device that utilizes quantum-tunneling phenomenon at metallic surfaces to obtain images of nanoscale structures

Schrӧdinger’s time-dependent equation

equation in space and time that allows us to determine wave functions of a quantum particle

Schrӧdinger’s time-independent equation

equation in space that allows us to determine wave functions of a quantum particle; this wave function must be multiplied by a time-modulation factor to obtain the time-dependent wave function

standing wave state

stationary state for which the real and imaginary parts of $\text{Ψ}(x,t)$ oscillate up and down like a standing wave (often modeled with sine and cosine functions)

state reduction

hypothetical process in which an observed or detected particle “jumps into” a definite state, often described in terms of the collapse of the particle’s wave function

stationary state

state for which the probability density function, ${\left|\text{Ψ}(x,t)\right|}^2$, does not vary in time

time-modulation factor

factor $e^{\text{−}i\omega t}$ that multiplies the time-independent wave function when the potential energy of the particle is time independent

transmission probability

also called tunneling probability, the probability that a particle will tunnel through a potential barrier

tunnel diode

electron tunneling-junction between two different semiconductors

tunneling probability

also called transmission probability, the probability that a particle will tunnel through a potential barrier

wave function

function that represents the quantum state of a particle (quantum system)

wave function collapse

equivalent to state reduction

wave packet

superposition of many plane matter waves that can be used to represent a localized particle