Quantum Mechanics - Theory Flashcards
Einstein proposed that an energy field radiating at frequency ν can be modeled as a collection of photons, each of energy ___________ (give the equation).
ε = hv
Where h = Planks constant = 6.626e-34 J-s
Boyd, NEGD, Pg. 54
Compton proposed that an energy field radiating at wavelength λ = c/v can be modeled as a collection of photons each having momentum ___________ (give the equation).
p = h/λ
Boyd, NEGD, Pg. 54
De Broglie proposed that a particle with energy ε and momentum p can be modeled as a wave with a frequency v = ________ and wavelength λ = ________.
v = ε/h
λ = h/p
Where h is Plank’s constant.
Body, NEGD, Pg 55
Describe a Fourier transformation.
The Fourier transform is a mathematical operation that transforms a function (often a time-domain signal) into its constituent frequencies. It’s a tool that decomposes a signal into the amplitudes of its sinusoidal components. In essence, it provides a way to move from the time domain to the frequency domain, allowing us to analyze the different frequency components of a given signal. The inverse does the opposite.
chatGPT
True or False
A takeaway from Heisenberg’s uncertainty principle is that to detect a particle, its properties must be changed.
True
Boyd, NEGD, Pg 56
State the correspondence principle.
Any quantum mechanical theory must satisfy the laws of classical physics in a regime where classical physics is valid.
Boyd, NEGD, Pg 57
What is the fundamental governing equation for quantum mechanics?
The Schrodinger Equation
Boyd, NEGD, Pg 57
The solution of the Schrodinger equation yields the _______.
Wave function
Boyd, NEGD, Pg 57
What is “degeneracy” in QM?
A situation where several energy states have the same energy level.
Boyd, NEGD, Pg 60
What does the phrase “eigenvalue problem” mean when said in relation to solving differential equations?
In the context of differential equations, the term “eigenvalue problem” generally refers to a class of problems where one seeks solutions that can be expressed as a product of two functions: one depending only on time and the other only on spatial variables. These solutions are of a special form, and the associated constants (eigenvalues) and functions (eigenfunctions) have special significance.
ChatGPT
True or False
The translational energy of a particle is quantized, and it can take on only certain clearly specified values.
True
Boyd, NEGD, Pg. 61
What is the “Hamiltonian” as it relates to classical mechanics?
The total energy of a given system.
H = KE + PE
Boyd, NEGD, Pg 62
A particle can take on different electronic energies when the electrons that surround its nucleus ____________.
Occupy different orbits.
Boyd, NEGD, Pg 68
What electronic configuration is the most stable?
The ground electronic state.
Boyd, NEGD, Pg 68
Heat transfer when radiation is a factor is governed by the _________.
(name of the relation and the equation)
Stephan Boltzmann Equation
P = σεT^4
Where
P = Power Density emitted, M/(s - m^2)
σ = Stephan-Boltzmann Constant
ε = The total emissivity
Molecular Physical Chemistry for Engineers, Yates, Pg. 39
Explain the total emissivity value (ε) as shown in the Stephan-Boltzmann law.
The value of ε is a measure of the efficiency of the reflection of radiated energy from the emitter body’s outer surface back into its interior.
A value of 1 is a perfect emitter, while 0 is a perfect reflector.
Molecular Physical Chemistry for Engineers, Yates, Pg. 39
True or False
One of the central postulates of wave mechanics is that the quantity ψ*ψ is proportional (for a given particle energy) to the number of particles that cross a unit area per unit time.
True.
Molecular Physical Chemistry for Engineers, Yates, Pg. 80
The time-independent wave function is associated with the _______ energy states of the quantum system.
Stationary
Molecular Physical Chemistry for Engineers, Yates, Pg. 82
True or False
The Schrodinger equation can be derived from other equations.
False. It is a fundamental equation which is assembled from postulates which are formulated from observation of nature.
Molecular Physical Chemistry for Engineers, Yates, Pg. 83
What is the operator for momentum? (give the equation)
\hat{p}_x = (hbar/i)∂/∂x = -ihbar(∂/∂x)
Molecular Physical Chemistry for Engineers, Yates, Pg. 83
True or False
The Schrodinger equation is an eigenvalue equation.
True
Molecular Physical Chemistry for Engineers, Yates, Pg. 85
Quantum mechanically allowed energies are referred to as _________.
Eigenstates.
Also sometimes called Eigenenergies.
Molecular Physical Chemistry for Engineers, Yates, Pg. 85
True or False
The wave function ψ, is the wave property of a particle that contains all of the information needed to describe the wavelength, KE, or momentum of a particle.
True.
Molecular Physical Chemistry for Engineers, Yates, Pg. 90
How did Max Born explain the physical meaning of the wave function?
He suggested that the wavefunction was closely related to the statistical probability of finding the particle within a given differential region of space.
Molecular Physical Chemistry for Engineers, Yates, Pg. 90
