### 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 $\text{\Psi}(x,t)$ 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, ${\left|\text{\Psi}(x,t)\right|}^{2}$, does not vary in time

- time-modulation factor
- factor ${e}^{\text{\u2212}i\omega t}$ 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