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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
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 Ψ(x,t)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, |Ψ(x,t)|2|Ψ(x,t)|2, does not vary in time
time-modulation factor
factor eiωteiωt 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
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