Quantum-Mechanical Theory of Molecular Polarizabilities - Revision history

Chrisb at 21:46, 8 July 2011

2011-07-08T21:46:22Z

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	<td style="text-align: center; width: 33%">[[Main_Page#Quantum Mechanical and Perturbation Theory of Polarizability \|Return to Quantum Mechanical and Perturbation Theory Menu]]</td>		<td style="text-align: center; width: 33%">[[Main_Page#Quantum Mechanical and Perturbation Theory of Polarizability \|Return to Quantum Mechanical and Perturbation Theory Menu]]</td>
	<td style="text-align: right; width: 33%">[[Dipole Moment\| Next Topic]]</td>		<td style="text-align: right; width: 33%">[[Mathematical Expansion of the Dipole Moment\| Next Topic]]</td>
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	<td style="text-align: center; width: 33%">[[Main_Page#Quantum Mechanical and Perturbation Theory of Polarizability \|Return to Quantum Mechanical and Perturbation Theory Menu]]</td>		<td style="text-align: center; width: 33%">[[Main_Page#Quantum Mechanical and Perturbation Theory of Polarizability \|Return to Quantum Mechanical and Perturbation Theory Menu]]</td>
	<td style="text-align: right; width: 33%">[[Dipole Moment\| Next Topic]]</td>		<td style="text-align: right; width: 33%">[[Mathematical Expansion of the Dipole Moment\| Next Topic]]</td>
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Chrisb at 19:51, 8 July 2011

2011-07-08T19:51:40Z

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	Also, note that n, mu and Epsilon are also complex quantities because they may involve both dispersion effects and attenuation effects. As soon as there is absorption, then that becomes an imaginary component to the expression. Thus, all of those are complex numbers.		Also, note that n, mu and Epsilon are also complex quantities because they may involve both dispersion effects and attenuation effects. As soon as there is absorption, then that becomes an imaginary component to the expression. Thus, all of those are complex numbers.

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			<td style="text-align: center; width: 33%">[[Main_Page#Quantum Mechanical and Perturbation Theory of Polarizability \|Return to Quantum Mechanical and Perturbation Theory Menu]]</td>
			<td style="text-align: right; width: 33%">[[Dipole Moment\| Next Topic]]</td>
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Chrisb at 19:46, 8 July 2011

2011-07-08T19:46:33Z

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	Quantum-Mechanical Theory of Molecular Polarizabilities up to Third Order		'''Quantum-Mechanical Theory of Molecular Polarizabilities up to Third Order'''

	The literature refers to first order, second order and third order polarizabilities. You may also see “first order hyperpolarizability “ which is the same thing as second order polarizability. These conventions may be confusing.		The literature refers to first order, second order and third order polarizabilities. You may also see “first order hyperpolarizability “ which is the same thing as second order polarizability. These conventions may be confusing.

Chrisb at 21:26, 28 June 2011

2011-06-28T21:26:58Z

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	<td style="text-align: center; width: 33%">[[Main_Page#Quantum Mechanical and Perturbation Theory of Polarizability \|Return to Quantum Mechanical and Perturbation Theory Menu]]</td>		<td style="text-align: center; width: 33%">[[Main_Page#Quantum Mechanical and Perturbation Theory of Polarizability \|Return to Quantum Mechanical and Perturbation Theory Menu]]</td>
	<td style="text-align: right; width: 33%">[[~~Electric~~ Dipole Moment\| Next Topic]]</td>		<td style="text-align: right; width: 33%">[[Dipole Moment\| Next Topic]]</td>
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Chrisb at 21:26, 28 June 2011

2011-06-28T21:26:34Z

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	<td style="text-align: center; width: 33%">[[Main_Page#Quantum Mechanical and Perturbation Theory of Polarizability \|Return to Quantum Mechanical and Perturbation Theory Menu]]</td>		<td style="text-align: center; width: 33%">[[Main_Page#Quantum Mechanical and Perturbation Theory of Polarizability \|Return to Quantum Mechanical and Perturbation Theory Menu]]</td>
	<td style="text-align: right; width: 33%">[[~~Perturbation Theory~~\| Next Topic]]</td>		<td style="text-align: right; width: 33%">[[Electric Dipole Moment\| Next Topic]]</td>
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Chrisb: /* Polarizablity to polarization */

2011-06-20T19:16:39Z

Polarizablity to polarization

← Older revision		Revision as of 12:16, 20 June 2011
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	where		where

	:<math>\~~epsilon_0~~\,\!</math> is the electric permittivity of a vacuum		:<math>\Epsilon_0\,\!</math> is the electric permittivity of a vacuum

	:<math>\Chi_{el}\,\!</math> is the electric susceptibility of the material; a tensor		:<math>\Chi_{el}\,\!</math> is the electric susceptibility of the material; a tensor

Chrisb: /* Polarizablity to polarization */

2011-06-20T19:16:06Z

Polarizablity to polarization

← Older revision		Revision as of 12:16, 20 June 2011
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	where		where

	:<math>\~~Epsilon_0~~\,\!</math> is the electric permittivity of a vacuum		:<math>\epsilon_0\,\!</math> is the electric permittivity of a vacuum

	:<math>\Chi_{el}\,\!</math> is the electric susceptibility of the material; a tensor		:<math>\Chi_{el}\,\!</math> is the electric susceptibility of the material; a tensor

Chrisb: /* Polarizablity to polarization */

2011-06-20T19:14:51Z

Polarizablity to polarization

← Older revision		Revision as of 12:14, 20 June 2011
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	At the microscopic (molecular) level, a molecule that can have a permanent dipole moment , mu0 (permanent dipole) will have an induced dipole moment when it is exposed to electric field (or the electric field of the light). That induced dipole moment is proportional to the electric field an alpha (the polarizability) and the electric field. Thus, we can extend the analogy by acknowledging that the larger the alpha, the larger the polarizability, and the larger the induced dipole moment.		At the microscopic (molecular) level, a molecule that can have a permanent dipole moment , mu0 (permanent dipole) will have an induced dipole moment when it is exposed to electric field (or the electric field of the light). That induced dipole moment is proportional to the electric field an alpha (the polarizability) and the electric field. Thus, we can extend the analogy by acknowledging that the larger the alpha, the larger the polarizability, and the larger the induced dipole moment.

	:<math>\overrightarrow{~~:<math>~~mu~~\,\!</math>~~} (induced) = \alpha \cdot \overrightarrow{E}\,\!</math>		:<math>\overrightarrow{\mu} (induced) = \alpha \cdot \overrightarrow{E}\,\!</math>

	where		where

Chrisb: /* Polarizablity to polarization */

2011-06-20T19:14:26Z

Polarizablity to polarization

← Older revision		Revision as of 12:14, 20 June 2011
Line 76:		Line 76:
	At the microscopic (molecular) level, a molecule that can have a permanent dipole moment , mu0 (permanent dipole) will have an induced dipole moment when it is exposed to electric field (or the electric field of the light). That induced dipole moment is proportional to the electric field an alpha (the polarizability) and the electric field. Thus, we can extend the analogy by acknowledging that the larger the alpha, the larger the polarizability, and the larger the induced dipole moment.		At the microscopic (molecular) level, a molecule that can have a permanent dipole moment , mu0 (permanent dipole) will have an induced dipole moment when it is exposed to electric field (or the electric field of the light). That induced dipole moment is proportional to the electric field an alpha (the polarizability) and the electric field. Thus, we can extend the analogy by acknowledging that the larger the alpha, the larger the polarizability, and the larger the induced dipole moment.

	:<math>\overrightarrow{μ} (induced) = \alpha \cdot \overrightarrow{E}\,\!</math>		:<math>\overrightarrow{:<math>mu\,\!</math>} (induced) = \alpha \cdot \overrightarrow{E}\,\!</math>

	where		where

Chrisb: /* Polarizablity to polarization */

2011-06-20T19:13:55Z

Polarizablity to polarization

← Older revision		Revision as of 12:13, 20 June 2011
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	At the microscopic (molecular) level, a molecule that can have a permanent dipole moment , mu0 (permanent dipole) will have an induced dipole moment when it is exposed to electric field (or the electric field of the light). That induced dipole moment is proportional to the electric field an alpha (the polarizability) and the electric field. Thus, we can extend the analogy by acknowledging that the larger the alpha, the larger the polarizability, and the larger the induced dipole moment.		At the microscopic (molecular) level, a molecule that can have a permanent dipole moment , mu0 (permanent dipole) will have an induced dipole moment when it is exposed to electric field (or the electric field of the light). That induced dipole moment is proportional to the electric field an alpha (the polarizability) and the electric field. Thus, we can extend the analogy by acknowledging that the larger the alpha, the larger the polarizability, and the larger the induced dipole moment.

	:<math>\overrightarrow{mu} (induced) = \alpha \cdot \overrightarrow{E}\,\!</math>		:<math>\overrightarrow{μ} (induced) = \alpha \cdot \overrightarrow{E}\,\!</math>

	where		where