1D & 3D PIB, DEGENERACY, ORTHOGONALITY Flashcards
WTF NALIMTAN NAKO HAHAHAHA
a concept that illustrates the behavior of a particle, such as an electron, confined to a specific region of space known as a box.
The Particle in a Box
In this model, the particle is assumed to be confined to a one dimensional box, meaning that it can only move along a _____________ and is _________ to escape from the box.
straight line,
unable
a mathematical function that describes the probability of finding the particle at any given point within the box.
wave function
The wave function of the particle is determined by the _______ and ______ of the box, as well as the energy of the particle.
size
shape
One of the key predictions of the particle in a box model is that the allowed energy levels of the particle are quantized, meaning that the particle can only have _______________, rather than any arbitrary energy.
certain specific energies
n is restricted to ______________.
positive integer
The energy of the particle in the box is
quantized , because the energy value is
______________ to having only certain values.
restricted
The symbol for the Laplacian operator is called _________
del-squared
The energy depends on a set of __________ and the sum of the squares of the
quantum numbers
constants
linearly independent wavefunctions that have the same energy are called ________________
degenerate
A system has not just a single wavefunction but many possible wavefunctions, each of which has an energy (obtained using an eigenvalue equation) and perhaps other eigenvalue observables
Orthogonality
two different wavefunctions were used in the above expression, the different wavefunctions have a property that requires that the integral be exactly zero
Orthogonality
The orthogonality and normality properties of wavefunctions are usually combined into a single expression termed __________________
orthonormality
orthonormality condition requires that no ____________ be present inside the integral.
operator
