Enumerated type - Revision history

122.164.224.206 at 13:39, 10 December 2014

2014-12-10T13:39:32Z

← Older revision		Revision as of 15:39, 10 December 2014
Line 1:		Line 1:
	~~The name of the author is Figures~~. ~~Hiring~~ is ~~her day job now~~ and she ~~will not alter~~ it ~~whenever soon~~. ~~One of the extremely very best issues~~ in ~~the globe for him is to collect badges but~~ he ~~is struggling to discover time for~~ it. ~~South Dakota~~ is exactly where me and ~~my husband reside~~.<br><br>my ~~web-site - std home test~~ ([http://~~www~~.~~reachoutsociety.info~~/~~user~~/~~JCondon visit here~~])		Hi there, I am Alyson Pomerleau and I believe it sounds quite good when you say it. As a woman what she really likes is fashion and she's been doing it for fairly a whilst. For years he's been residing in Alaska and he doesn't plan on altering it. Distributing manufacturing is exactly where my primary earnings comes from and it's some accurate [http://www.youronlinepublishers.com/authWiki/AdolphvhBladenqq online psychic reading] readings, [http://www.aseandate.com/index.php?m=member_profile&p=profile&id=13352970 just click the up coming page], thing I really enjoy.<br><br>Also visit my website ... certified psychics ([http://kpupf.com/xe/talk/735373 kpupf.com])

en>Lipsio: Sub-sectioned C, Paschal, and Perl. Changed a couple of pronouns from second person to impersonal.

2014-02-06T23:48:21Z

Sub-sectioned C, Paschal, and Perl. Changed a couple of pronouns from second person to impersonal.

← Older revision		Revision as of 01:48, 7 February 2014
Line 1:		Line 1:
	'''Fermi heap''' and '''Fermi hole''' refer to two closely related [[quantum physics\|quantum]] [[phenomenon\|phenomena]] that occur in many-electron atoms. They arise due to the [[Pauli exclusion principle]], according to which no two electrons can be in the same quantum state in a system (which, accounting for electrons' [[Spin (physics)\|spin]], means that there can be up to two electrons in the same [[Atomic orbital\|orbital]]). Due to [[indistinguishability]] of ~~elementary particles,~~ the probability of a [[Measurement in quantum mechanics\|measurement]] yielding a certain [[eigenvalue]] must be invariant when electrons are exchanged, which means that the [[probability amplitude]] must either remain the same or change sign. ~~For instance, consider an excited state of the helium atom in which electron 1~~ is ~~in the 1s orbital~~ and ~~electron 2 has been excited to the 2s orbital. It is~~ not possible, even in principle, to distinguish electron 1 from electron 2. In other words, electron 2 might be in the 1s orbital with electron 1 in the 2s orbital. As they are [[fermions]], electrons must be described by an [[Symmetry (physics)\|anti-symmetric]] wavefunction which must change sign under electron exchange, resulting in either a [[Enrico Fermi\|Fermi]] hole (having a lower probability of being found close to each other) or a [[Enrico Fermi\|Fermi]] heap (having a higher probability of being found close to each other). ~~Since electrons repel one another electrically, Fermi holes and Fermi heaps have drastic effects on the energy~~ of ~~many-electron atoms, although~~ the ~~effect can be illustrated~~ in the ~~case of the [[helium atom]].~~		The name of the author is Figures. Hiring is her day job now and she will not alter it whenever soon. One of the extremely very best issues in the globe for him is to collect badges but he is struggling to discover time for it. South Dakota is exactly where me and my husband reside.<br><br>my web-site - std home test ([http://www.reachoutsociety.info/user/JCondon visit here])

	Neglecting the [[spin-orbit interaction]], the wavefunction for the two electrons can be written as <math>\Psi = \Psi_0 \Psi_s</math>, where we have split the wavefunction into spatial and spin parts. As mentioned above, <math>\Psi</math> needs to be antisymmetric, and so the antisymmetry can arise either from the spin part or the spatial part. There are 4 possible [[spin quantum number\|spin]] states for ~~this system:~~

	~~<math>\chi_+(1)\chi_+(2)</math>~~

	~~<math>\chi_-(1)\chi_-(2)</math>~~

	~~<math>\chi_+(1)\chi_-(2)</math>~~

	~~<math>\chi_-(1)\chi_+(2)</math>~~

	~~However, only the first two are symmetric or anti-symmetric to electron exchange (which corresponds to exchanging 1 and 2). The last two need to be rewritten as:~~

	~~<math>\chi_{1,1} = \chi_+(1)\chi_+(2)</math>~~

	~~<math>\chi_{1,-1} = \chi_-(1)\chi_-(2)</math>~~

	~~<math>\chi_{1,0} = \frac{1}{\sqrt{2}} (\chi_-(1)\chi_+(2)+\chi_+(1)\chi_-(2))</math>~~

	~~<math>\chi_{0,0} = \frac{1}{\sqrt{2}} (\chi_-(1)\chi_+(2)-\chi_+(1)\chi_-(2))</math>~~

	~~The first three are symmetric, whereas the last one is anti-symmetric. Say one of the electrons in the helium atom~~ is ~~excited to the 2s state. In this case, its spatial wavefunction will have~~ to ~~be either anti-symmetric (requiring a symmetric spin wavefunction):~~

	~~<math>\Psi_{0} = \psi_{1s} (1) \psi_{2s} (2) - \psi_{2s} (1) \psi_{1s} (2)</math>~~

	~~Or symmetric (requiring an anti-symmetric spin wavefunction):~~

	~~<math>\Psi_{0} = \psi_{1s} (1) \psi_{2s} (2) + \psi_{2s} (1) \psi_{1s} (2)</math>~~

	~~In the first case, the possible spin states are the three symmetric ones listed above, and this state~~ is ~~commonly referred~~ to ~~as a ''triplet''~~. ~~The triplet state~~ is ~~not allowed in the ground state of the helium atom, since the spatial function in this case is symmetric~~ and ~~the spin function needs to be anti-symmetric~~. ~~We can observe that if we take~~ <~~math~~>~~\psi_{1s} \approx \psi_{2s}~~<~~/math~~>~~, the probability amplitude tends to zero, meaning that the electrons are unlikely to be close to each other, which is referred to as Fermi hole and is responsible for the space~~-~~occupying properties of matter.~~

	Similarly, in the second case, there is only one possible spin state, <math>\chi_{0,0}</math>, and so this state is commonly referred to as a ''singlet''. We can also observe that the probability amplitude is higher when electrons are close to each other, which means that it is slightly more likely that the electrons will be observed together. This phenomenon is referred to as Fermi heap, and plays an important role in [[chemical bond]]ing by allowing both electrons to be localized in the internuclear region and thus shielding the positively charged nuclei from electrostatic repulsion with one another.

	~~Since electrons repel one another, Fermi holes and Fermi heaps have drastic effects on the energy of many~~-electron atoms, such as the periodic properties of the elements. Since bringing electrons together requires doing work, Fermi heaps have higher energy than Fermi holes. This result is generalized in terms of multiplicity by [[Hund's rule]] which states that the higher the spin multiplicity of a state (~~number of spin states it is allowed to have by the exclusion principle), the lower its energy will be.~~

	~~Animations of Fermi holes and Fermi heaps in the carbon atom are here.<ref name="Dill2">Dill, Dan,~~ [http://~~quantum~~.bu.~~edu/notes/GeneralChemistry~~/~~FermniHolesAndHeaps.html Fermi holes and Fermi heaps]. URL checked 18 June 2009<~~/~~ref> Details of the origin and significance of Fermi holes and Fermi heaps in the structure of atoms are discussed~~ here~~.<ref name="Dill">Dill, Dan, [http://quantum.bu.edu/notes/GeneralChemistry/03-5-FermiHolesAndHeaps.pdf Many-electron atoms: Fermi holes and Fermi heaps~~]~~. URL checked 18 June 2009</ref>~~

	~~==References==~~
	~~<references />~~

	*{{cite book \| author=Dill, Dan \| title=Notes on General Chemistry (2nd ed.)~~, Chapter 3.5, Many-electron atoms: Fermi holes and Fermi heaps \| publisher=W. H. Freeman \| year=2006 \| isbn=0-393-97661-0 }}~~
	~~<!--[[User:Zoedill\|Dan Dill]] 19:49, 10 November 2006 (UTC) <br />~~
	~~--[[User:NinurtaDB\|Daniel Barr]] 21:26, 12 January 2007-->~~

	~~{{DEFAULTSORT:Fermi Hole}}~~
	~~[[Category:Quantum mechanics]]~~
	~~[[Category:Enrico Fermi\|Heap and hole]]~~

24.96.180.44: 'necessarily' may imply to some that distinctness is necessary--which is inconsitent with the last part of the sentence. This change eliminates any potential confusion.

2014-02-02T05:22:47Z

'necessarily' may imply to some that distinctness is necessary--which is inconsitent with the last part of the sentence. This change eliminates any potential confusion.

← Older revision		Revision as of 07:22, 2 February 2014
Line 1:		Line 1:
	The ~~person who wrote~~ the ~~post~~ is ~~called Jayson Hirano~~ and ~~he totally digs~~ that ~~title~~. ~~Invoicing~~ is ~~what I do for~~ a ~~living but I~~'~~ve usually needed my personal company. I~~'~~ve usually loved residing in Kentucky but now I~~'~~m considering~~ other ~~choices~~. ~~I am really fond of~~ to go to ~~karaoke but I~~'~~ve been using on new things lately~~.<br><br>~~My blog post: clairvoyance -~~ [http://~~kard~~.dk/?p=~~24252 click here to read~~] -		'''Fermi heap''' and '''Fermi hole''' refer to two closely related [[quantum physics\|quantum]] [[phenomenon\|phenomena]] that occur in many-electron atoms. They arise due to the [[Pauli exclusion principle]], according to which no two electrons can be in the same quantum state in a system (which, accounting for electrons' [[Spin (physics)\|spin]], means that there can be up to two electrons in the same [[Atomic orbital\|orbital]]). Due to [[indistinguishability]] of elementary particles, the probability of a [[Measurement in quantum mechanics\|measurement]] yielding a certain [[eigenvalue]] must be invariant when electrons are exchanged, which means that the [[probability amplitude]] must either remain the same or change sign. For instance, consider an excited state of the helium atom in which electron 1 is in the 1s orbital and electron 2 has been excited to the 2s orbital. It is not possible, even in principle, to distinguish electron 1 from electron 2. In other words, electron 2 might be in the 1s orbital with electron 1 in the 2s orbital. As they are [[fermions]], electrons must be described by an [[Symmetry (physics)\|anti-symmetric]] wavefunction which must change sign under electron exchange, resulting in either a [[Enrico Fermi\|Fermi]] hole (having a lower probability of being found close to each other) or a [[Enrico Fermi\|Fermi]] heap (having a higher probability of being found close to each other). Since electrons repel one another electrically, Fermi holes and Fermi heaps have drastic effects on the energy of many-electron atoms, although the effect can be illustrated in the case of the [[helium atom]].

			Neglecting the [[spin-orbit interaction]], the wavefunction for the two electrons can be written as <math>\Psi = \Psi_0 \Psi_s</math>, where we have split the wavefunction into spatial and spin parts. As mentioned above, <math>\Psi</math> needs to be antisymmetric, and so the antisymmetry can arise either from the spin part or the spatial part. There are 4 possible [[spin quantum number\|spin]] states for this system:

			<math>\chi_+(1)\chi_+(2)</math>

			<math>\chi_-(1)\chi_-(2)</math>

			<math>\chi_+(1)\chi_-(2)</math>

			<math>\chi_-(1)\chi_+(2)</math>

			However, only the first two are symmetric or anti-symmetric to electron exchange (which corresponds to exchanging 1 and 2). The last two need to be rewritten as:

			<math>\chi_{1,1} = \chi_+(1)\chi_+(2)</math>

			<math>\chi_{1,-1} = \chi_-(1)\chi_-(2)</math>

			<math>\chi_{1,0} = \frac{1}{\sqrt{2}} (\chi_-(1)\chi_+(2)+\chi_+(1)\chi_-(2))</math>

			<math>\chi_{0,0} = \frac{1}{\sqrt{2}} (\chi_-(1)\chi_+(2)-\chi_+(1)\chi_-(2))</math>

			The first three are symmetric, whereas the last one is anti-symmetric. Say one of the electrons in the helium atom is excited to the 2s state. In this case, its spatial wavefunction will have to be either anti-symmetric (requiring a symmetric spin wavefunction):

			<math>\Psi_{0} = \psi_{1s} (1) \psi_{2s} (2) - \psi_{2s} (1) \psi_{1s} (2)</math>

			Or symmetric (requiring an anti-symmetric spin wavefunction):

			<math>\Psi_{0} = \psi_{1s} (1) \psi_{2s} (2) + \psi_{2s} (1) \psi_{1s} (2)</math>

			In the first case, the possible spin states are the three symmetric ones listed above, and this state is commonly referred to as a ''triplet''. The triplet state is not allowed in the ground state of the helium atom, since the spatial function in this case is symmetric and the spin function needs to be anti-symmetric. We can observe that if we take <math>\psi_{1s} \approx \psi_{2s}</math>, the probability amplitude tends to zero, meaning that the electrons are unlikely to be close to each other, which is referred to as Fermi hole and is responsible for the space-occupying properties of matter.

			Similarly, in the second case, there is only one possible spin state, <math>\chi_{0,0}</math>, and so this state is commonly referred to as a ''singlet''. We can also observe that the probability amplitude is higher when electrons are close to each other, which means that it is slightly more likely that the electrons will be observed together. This phenomenon is referred to as Fermi heap, and plays an important role in [[chemical bond]]ing by allowing both electrons to be localized in the internuclear region and thus shielding the positively charged nuclei from electrostatic repulsion with one another.

			Since electrons repel one another, Fermi holes and Fermi heaps have drastic effects on the energy of many-electron atoms, such as the periodic properties of the elements. Since bringing electrons together requires doing work, Fermi heaps have higher energy than Fermi holes. This result is generalized in terms of multiplicity by [[Hund's rule]] which states that the higher the spin multiplicity of a state (number of spin states it is allowed to have by the exclusion principle), the lower its energy will be.

			Animations of Fermi holes and Fermi heaps in the carbon atom are here.<ref name="Dill2">Dill, Dan, [http://quantum.bu.edu/notes/GeneralChemistry/FermniHolesAndHeaps.html Fermi holes and Fermi heaps]. URL checked 18 June 2009</ref> Details of the origin and significance of Fermi holes and Fermi heaps in the structure of atoms are discussed here.<ref name="Dill">Dill, Dan, [http://quantum.bu.edu/notes/GeneralChemistry/03-5-FermiHolesAndHeaps.pdf Many-electron atoms: Fermi holes and Fermi heaps]. URL checked 18 June 2009</ref>

			==References==
			<references />

			*{{cite book \| author=Dill, Dan \| title=Notes on General Chemistry (2nd ed.), Chapter 3.5, Many-electron atoms: Fermi holes and Fermi heaps \| publisher=W. H. Freeman \| year=2006 \| isbn=0-393-97661-0 }}
			<!--[[User:Zoedill\|Dan Dill]] 19:49, 10 November 2006 (UTC) <br />
			--[[User:NinurtaDB\|Daniel Barr]] 21:26, 12 January 2007-->

			{{DEFAULTSORT:Fermi Hole}}
			[[Category:Quantum mechanics]]
			[[Category:Enrico Fermi\|Heap and hole]]

217.155.120.113: Moved Fortran up a level, it is not syntactically similar to C

2012-08-09T11:20:13Z

Moved Fortran up a level, it is not syntactically similar to C

New page

The person who wrote the post is called Jayson Hirano and he totally digs that title. Invoicing is what I do for a living but I've usually needed my personal company. I've usually loved residing in Kentucky but now I'm considering other choices. I am really fond of to go to karaoke but I've been using on new things lately.<br><br>My blog post: clairvoyance - [http://kard.dk/?p=24252 click here to read] -