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Book Chapter
Series: AIPP Books, Methods
Published: November 2022
10.1063/9780735422575_009
EISBN: 978-0-7354-2257-5
ISBN: 978-0-7354-2254-4
...Introduction We are going to derive the main formulas for the ionized wavepacket and the associated transition amplitudes when an atomic system is placed in a weak field. Evaluating these formulas requires the details of the atomic structure, but at a certain level we can discuss it more generally...
Images
Left: schematic of energy domain of an ionized <span class="search-highlight">wavepacket</span> from a weak-field...
Published: November 2022
FIG. 9.2 Left: schematic of energy domain of an ionized wavepacket from a weak-field pulse; γL ≃ 1/τL. Right: H 2 + ionization with pulse polarized linearly along its internuclei quantization axis. More about this image found in Left: schematic of energy domain of an ionized wavepacket from a weak-field...
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Ionization <span class="search-highlight">wavepacket</span> released following interaction of hydrogen molecular ...
Published: November 2022
FIG. 9.3 Ionization wavepacket released following interaction of hydrogen molecular ion H 2 + with a pulse (40 eV, 1013 W/cm2, 24 cycles, Hann). The horizontal axis represents the position along the symmetry axis of the system (z axis) after a 24-cycle laser pulse and post-propagation of 3.5 times the length of the pulse. For the calculation, the full TDSE was propagated. The position of the first peak confirms the approximate relation z = kLtd. More about this image found in Ionization wavepacket released following interaction of hydrogen molecular ...
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Images
Simplified sketch of ionization process. A pulse <em>E</em>(<italic
Published: November 2022
FIG. 9.1 Simplified sketch of ionization process. A pulse E(t) is impinging on an isolated atom, and an electronic wavepacket is released. A detector placed at a far distance and at a solid angle Ωr = (θ, ϕ) counts the electrons per unit time; this counting is related closely to the electronic radial current jrr; t). The laser pulse and the electronic current are varying in both space and time (not to scale in the figure). More about this image found in Simplified sketch of ionization process. A pulse E(
Book Chapter
Series: AIPP Books, Methods
Published: November 2022
10.1063/9780735422575_006
EISBN: 978-0-7354-2257-5
ISBN: 978-0-7354-2254-4
... are of direct relevance here, only those that in the remote future lead to an outgoing wavepacket located far from the atomic region. This brings to the forefront the question of what are the appropriate boundary conditions at the far end of the solution’s configuration space. Boundary conditions (BCs...
Book
Book Cover Image
Series: AIPP Books, Methods
Published: November 2022
10.1063/9780735422575
EISBN: 978-0-7354-2257-5
ISBN: 978-0-7354-2254-4
Book Chapter
Series: AIPP Books, Methods
Published: November 2022
0
EISBN: 978-0-7354-2257-5
ISBN: 978-0-7354-2254-4
... and window operator methods ,” Phys. Rev. A   102 , 023101 ( 2020 ). 10.1103/PhysRevA.102.023101 Madsen , L. B. , Nikolopoulos , L. A. A. , Kjeldsen , T. K. , and Fernandez , J. , “ Extracting continuum information from Ψ(t) in time-dependent wavepacket calculations ,” Phys. Rev...
Book Chapter
Series: AIPP Books, Methods
Published: November 2022
10.1063/9780735422575_010
EISBN: 978-0-7354-2257-5
ISBN: 978-0-7354-2254-4
...) for the measurement to occur; so in the asymptotic region, we have k ≃ k r , and this justifies Ω ^ r = Ω ^ k . Finally, note also that if the observation time τd is so large that the electronic (localized) wavepacket is far from the interaction region...
Book Chapter
Series: AIPP Books, Methods
Published: November 2022
10.1063/9780735422575_001
EISBN: 978-0-7354-2257-5
ISBN: 978-0-7354-2254-4
... distributions: in the remote past when the interaction term is not present, the system is in any one of the eigenstates of H ^ 0 (or in any combination of them, a wavepacket), and then the interaction term switches on and changes the system’s Hamiltonian, causing a time development...
Book Chapter
Series: AIPP Books, Methods
Published: November 2022
10.1063/9780735422575_008
EISBN: 978-0-7354-2257-5
ISBN: 978-0-7354-2254-4
... ) , and in view of ( 8.16 ) in terms of χ(r, t), this applies both during and long after the interaction. The pulse has a bandwidth of frequencies, and because of this it will generally excite a wavepacket in the continuum (apart from any bound states that may have been...
Book Chapter
Series: AIPP Books, Methods
Published: November 2022
10.1063/9780735422575_004
EISBN: 978-0-7354-2257-5
ISBN: 978-0-7354-2254-4
... are left with a vector with ca. 39 880 components that are zero and that a priori will contribute nothing in the H ^ y 0 matrix-vector calculation. Of course, as the wavepacket is forming, these components start to be populated, and only then does it make sense to use them...
Images
Superposition of a large number of harmonic plane waves of slightly differe...
Published: May 2022
FIG. 5.3 Superposition of a large number of harmonic plane waves of slightly different frequencies and different amplitudes, resulting in a spatially confined wavepacket. More about this image found in Superposition of a large number of harmonic plane waves of slightly differe...
Book Chapter
Series: AIPP Books, Principles
Published: May 2022
10.1063/9780735424517_008
EISBN: 978-0-7354-2451-7
ISBN: 978-0-7354-2448-7
... specific mode of light. On the other hand, the coherent state is close to the quantum harmonic oscillator (counterpart of a classical harmonic oscillator). Unlike the classical harmonic oscillator, a quantum harmonic oscillator wavepacket preserves its shape while undergoing harmonic oscillation...
Book Chapter
Series: AIPP Books, Principles
Published: May 2022
10.1063/9780735424517_005
EISBN: 978-0-7354-2451-7
ISBN: 978-0-7354-2448-7
..., they knock-off electrons from its surface. This states that light is absorbed in packets as if they are made up of particles. Specifically, the process is observed when the frequency of light is greater than a threshold. So, wavepackets/quanta of energy must be greater for knocking off the electrons...
Book Chapter
Series: AIPP Books, Principles
Published: May 2022
10.1063/9780735424517_007
EISBN: 978-0-7354-2451-7
ISBN: 978-0-7354-2448-7
.... This will be the subject matter of the subsequent section. Physical Interpretation of the Coherent State The wavefunction ϕn(q) can be interpreted as a wavepacket undergoing simple harmonic motion. Such a wavefunction represents closely to a classical field. Consider...
Book
Book Cover Image
Series: AIPP Books, Principles
Published: May 2022
10.1063/9780735424517
EISBN: 978-0-7354-2451-7
ISBN: 978-0-7354-2448-7