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- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Nonlinear_and_Two-Dimensional_Spectroscopy_(Tokmakoff)/00%3A_Front_Matter/04%3A_IntroductionWe can imagine studying these spectral features as a function of control variables for the light field (amplitude, frequency, polarization, phase, etc.) or for the sample (for instance a systematic va...We can imagine studying these spectral features as a function of control variables for the light field (amplitude, frequency, polarization, phase, etc.) or for the sample (for instance a systematic variation of the physical properties of the sample).
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Nonlinear_and_Two-Dimensional_Spectroscopy_(Tokmakoff)/zz%3A_Back_Matter
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Time_Dependent_Quantum_Mechanics_and_Spectroscopy_(Tokmakoff)/05%3A_The_Density_MatrixThe density matrix or density operator is an alternate representation of the state of a quantum system for which we have previously used the wavefunction. Although describing a quantum system with the...The density matrix or density operator is an alternate representation of the state of a quantum system for which we have previously used the wavefunction. Although describing a quantum system with the density matrix is equivalent to using the wavefunction, one gains significant practical advantages using the density matrix for certain time-dependent problems—particularly relaxation and nonlinear spectroscopy in the condensed phase.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Time_Dependent_Quantum_Mechanics_and_Spectroscopy_(Tokmakoff)/03%3A__Time-Evolution_Operator/3.04%3A_Resonant_Driving_of_a_Two-Level_SystemLet’s describe what happens when you drive a two-level system with an oscillating potential. Note, this is the form you would expect for an electromagnetic field interacting with charged particles, i....Let’s describe what happens when you drive a two-level system with an oscillating potential. Note, this is the form you would expect for an electromagnetic field interacting with charged particles, i.e. dipole transitions. In a simple sense, the electric field is
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Time_Dependent_Quantum_Mechanics_and_Spectroscopy_(Tokmakoff)I would like to thank a number of colleagues and prior instructors who were the source of content that guided my preparation of several of these lectures, including Bob Silbey, Keith Nelson, Troy Van ...I would like to thank a number of colleagues and prior instructors who were the source of content that guided my preparation of several of these lectures, including Bob Silbey, Keith Nelson, Troy Van Voorhis, Bob Field, John Ross and Graham Fleming. I also want to thank Anne Hudson, Peter Giunta, and Tanya Shpigel for their assistance preparing the notes over the years, and the Department of Energy and National Science Foundation for their ongoing support of my research in this area.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Time_Dependent_Quantum_Mechanics_and_Spectroscopy_(Tokmakoff)/08%3A_Mixed_States_and_the_Density_MatrixMolecules in dense media interact with one another, and as a result no two molecules have the same state. Energy placed into one degree of freedom will ultimately leak irreversibly into its environmen...Molecules in dense media interact with one another, and as a result no two molecules have the same state. Energy placed into one degree of freedom will ultimately leak irreversibly into its environment. We cannot write down an exact Hamiltonian for these problems; however, we can concentrate on a few degrees of freedom that are observed in a measurement, and try and describe the influence of the surroundings in a statistical manner.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Time_Dependent_Quantum_Mechanics_and_Spectroscopy_(Tokmakoff)/04%3A_Irreversible_RelaxationIf one reverses the sign of time and thereby momenta of objects, we should be able to go back where the system was at an earlier time. We can see this in the exact solution to the two-level problem, w...If one reverses the sign of time and thereby momenta of objects, we should be able to go back where the system was at an earlier time. We can see this in the exact solution to the two-level problem, where amplitude oscillates between the two states with a frequency that depends on the coupling. In contrast, when a quantum system is in contact with another system having many degrees of freedom, a definite direction emerges to the arrow of time, and the system’s dynamics is no longer reversible.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Time_Dependent_Quantum_Mechanics_and_Spectroscopy_(Tokmakoff)/07%3A_Interaction_of_Light_and_Matter/7.02%3A_Classical_LightMatter_InteractionsAs a starting point, it is helpful to first summarize the classical description of electromagnetic fields.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Time_Dependent_Quantum_Mechanics_and_Spectroscopy_(Tokmakoff)/03%3A__Time-Evolution_Operator/3.07%3A_Time-Dependent_Perturbation_TheoryPerturbation theory refers to calculating the time-dependence of a system by truncating the expansion of the interaction picture time-evolution operator after a certain term. In practice, truncating t...Perturbation theory refers to calculating the time-dependence of a system by truncating the expansion of the interaction picture time-evolution operator after a certain term. In practice, truncating the full time-propagator U is not effective, and only works well for times short compared to the inverse of the energy splitting between coupled states of your Hamiltonian.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Nonlinear_and_Two-Dimensional_Spectroscopy_(Tokmakoff)/01%3A_Coherent_Spectroscopy_and_the_Nonlinear_PolarizationHere we note the oscillating polarization is proportional to the signal field, although there is a π/2 phase shift between the two, \(\bar E_{sig}\propto i \bar P\), because in the sample the polariza...Here we note the oscillating polarization is proportional to the signal field, although there is a π/2 phase shift between the two, \(\bar E_{sig}\propto i \bar P\), because in the sample the polarization is related to the gradient of the field.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Time_Dependent_Quantum_Mechanics_and_Spectroscopy_(Tokmakoff)/13%3A_Coupling_of_Electronic_and_Nuclear_Motion/13.03%3A_Semiclassical_Approximation_to_the_Dipole_Correlation_FunctionThe semiclassical approximation is a useful representation of the dipole correlation function when one wants to describe the dark degrees of freedom (the bath) using classical molecular dynamics simul...The semiclassical approximation is a useful representation of the dipole correlation function when one wants to describe the dark degrees of freedom (the bath) using classical molecular dynamics simulations.
