Vật lí bán dẫn
Posted by Gin | Posted in Tài liệu tham khảo | Posted on 1/02/2010 08:35:00 CH
Đây là tài liệu mà admin đã tìm được trong quá trình sưu tầm tài liệu về " Vật lí bán dẫn" - mặc dù là tại liệu tiếng Anh, nhưng mong các bạn nghiên cứu tư dịch để có thêm kiến thức, về phần BQT cũng sẽ có 1 bản dịch để chúng ta trao đổi, so sánh và trao dồi khả năng tiếng Anh của mình...mong các bạn có ý kiến và ủng hộ
Thân
In physics, the exchange interaction is a quantum mechanical effect which increases or decreases the expectation value of the energy or distance between two or more identical particles when their wave funtions overlap. For example, the exchange interaction results in identical particles with spatially symmetric wave functions appearing “closer together” than would be expected of distinguishable particles, and in identical particles with spatially antisymmetric wave funtions appearing “farther apart”
Although one might naively expect such an interaction to result from a force, the exchange interaction is a purely quantum mechanical effect without any analog in classical mechanics. It is the result of the fact that the wave function of indistinguishable is subject to exchange symmetry, that is, the wave function describing two particles that can not be distinguished must be either unchanged (symmetric) or inverted in sign (antisymmetric) if the labels of the two particles are changed
For example, if the expectation value of the distance between two particles in a spatially symmetric or antisymmetric state is calculated, the exchange interaction may be seen
Both bosons anh fermions can experience the exchange interaction provided that the particles in question indistinguishable
The exchange interaction is sometimes called the exchange force, but it is not a true force and should not be confused with the exchange forces produced by the exchange of force carriers, such as the electromagnetic force produced between two electrons by the exchange of a photon, or the strong force between two quarks produced by the exchange of a gluon.
Quantum mechanical particels are classified as bosons or fermions. The spin-statistics theorem of quantum field theory demands that all particles with half-integer spin behave as fermions and all particles with integer spin behave as bosons. Multiple bosons may occupy the same quantum state, by the Pauli exclusion principle, however, no two fermions can occupy the same state. Since electrons have spin ½ , they are fermions. This means that the overall warefunction of a system must be antisymmetric when two electrons are exchanged.
Taking a system with two electrons, we may attempt to model the state of each electron by first assuming the electrons behave independently, and taking wavefunction in position space of …….. for the first electrons……….. . We assume that…. And ….. are orthogonal, and that each corresponds to an energy eigenstate of its electron. Now, if if the overall system have spin 1, the spin wave funtions is symmetric , and we may contruct a wavefunction for the overall system in position space by using an antisymmetric combination of the product wavefunction in position space.
On the other hand, if the overall system has spin 0, the spin wave function is antisymmetric, and we may therefore construct the overall position-space wavefunction by using a symmetric combination of the product wavefunctions in position space
If we assume that the interaction energy between the two electrons,…………, is symmetric, and restrict our attention to the vector space spanned by ….. and …. , then each of these wavefunctions will yield eigenstates for the system energy, and the difference between their energies will be
Taking into account the different joint spins of these eigenstates, we may model this difference by adding a spin-spin interaction term
To the Hamiltonian, where S1 and S2 are the spin operators of the two electrons. This term, often referred to as the HH, gives one form of the exchange interaction
When J is positive, the exchange energy favors electrons with parallel spins, this is a primary cause of ferromagnetism in material such as iron. In fact, when the interaction V1 is purely due to Coulomd repulsion of electrons……………… , J is always positive ( unless the wavefunction do not overlap at all, in which case J is zero)
When J is negative, the interaction favors electrons with antiparallel spins, potentially causing antiferromagnetism
Although these consequences of the exchange interaction are magnetic in nature, the cause is not, it is due primarily to electric repulsion, and the Pauli exclusion principle. Indeed, in general, the direct magnetic interaction between a pair of electrons ( due to their electron magnetic moments) is negligibly small compared to this electric interaction
Exchange energy splittings are very elusive to calculate for molecular systems at large internuclear distances. However, analytical formulae have been worked out for the hydrogen molecular iron ( see references herein)
Thân
In physics, the exchange interaction is a quantum mechanical effect which increases or decreases the expectation value of the energy or distance between two or more identical particles when their wave funtions overlap. For example, the exchange interaction results in identical particles with spatially symmetric wave functions appearing “closer together” than would be expected of distinguishable particles, and in identical particles with spatially antisymmetric wave funtions appearing “farther apart”
Although one might naively expect such an interaction to result from a force, the exchange interaction is a purely quantum mechanical effect without any analog in classical mechanics. It is the result of the fact that the wave function of indistinguishable is subject to exchange symmetry, that is, the wave function describing two particles that can not be distinguished must be either unchanged (symmetric) or inverted in sign (antisymmetric) if the labels of the two particles are changed
For example, if the expectation value of the distance between two particles in a spatially symmetric or antisymmetric state is calculated, the exchange interaction may be seen
Both bosons anh fermions can experience the exchange interaction provided that the particles in question indistinguishable
The exchange interaction is sometimes called the exchange force, but it is not a true force and should not be confused with the exchange forces produced by the exchange of force carriers, such as the electromagnetic force produced between two electrons by the exchange of a photon, or the strong force between two quarks produced by the exchange of a gluon.
Quantum mechanical particels are classified as bosons or fermions. The spin-statistics theorem of quantum field theory demands that all particles with half-integer spin behave as fermions and all particles with integer spin behave as bosons. Multiple bosons may occupy the same quantum state, by the Pauli exclusion principle, however, no two fermions can occupy the same state. Since electrons have spin ½ , they are fermions. This means that the overall warefunction of a system must be antisymmetric when two electrons are exchanged.
Taking a system with two electrons, we may attempt to model the state of each electron by first assuming the electrons behave independently, and taking wavefunction in position space of …….. for the first electrons……….. . We assume that…. And ….. are orthogonal, and that each corresponds to an energy eigenstate of its electron. Now, if if the overall system have spin 1, the spin wave funtions is symmetric , and we may contruct a wavefunction for the overall system in position space by using an antisymmetric combination of the product wavefunction in position space.
On the other hand, if the overall system has spin 0, the spin wave function is antisymmetric, and we may therefore construct the overall position-space wavefunction by using a symmetric combination of the product wavefunctions in position space
If we assume that the interaction energy between the two electrons,…………, is symmetric, and restrict our attention to the vector space spanned by ….. and …. , then each of these wavefunctions will yield eigenstates for the system energy, and the difference between their energies will be
Taking into account the different joint spins of these eigenstates, we may model this difference by adding a spin-spin interaction term
To the Hamiltonian, where S1 and S2 are the spin operators of the two electrons. This term, often referred to as the HH, gives one form of the exchange interaction
When J is positive, the exchange energy favors electrons with parallel spins, this is a primary cause of ferromagnetism in material such as iron. In fact, when the interaction V1 is purely due to Coulomd repulsion of electrons……………… , J is always positive ( unless the wavefunction do not overlap at all, in which case J is zero)
When J is negative, the interaction favors electrons with antiparallel spins, potentially causing antiferromagnetism
Although these consequences of the exchange interaction are magnetic in nature, the cause is not, it is due primarily to electric repulsion, and the Pauli exclusion principle. Indeed, in general, the direct magnetic interaction between a pair of electrons ( due to their electron magnetic moments) is negligibly small compared to this electric interaction
Exchange energy splittings are very elusive to calculate for molecular systems at large internuclear distances. However, analytical formulae have been worked out for the hydrogen molecular iron ( see references herein)
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