Quantum in physics Coursework Example | Topics and Well Written Essays - 1000 words

Quantum in physics - Coursework Example (Belloni et al, 2005) Local density Approximation (LDA) Exchange correlation (XC) is the relationship between different electrons and the exchange of energy in the electronic setup of a particular quantum system. Further density functional theory (DFT) is study of an electronic structure when it is at its least excited state called the ground state or the zero-point energy of the system. Electron density is defined as the probability of an electron filling up a miniscule space around any particular point. It is denoted by n(r). (Computational Materials Science Group,1998) Local Density approximation can now be defined as an approximation of the exchange correlation in the Density functional theory or in other words the energy relationship between different electrons in an electronic structure at ground state. This can be found out using a function of the electron density at each spatial point. Further Homogeneous electron gas (HEG) is the interaction of positive atomic nuclei that ar e uniformly distributed in space with the negatively charged electrons that have a uniform density in the same space. Local Density approximations are thus most accurately derived when functional integrals are made on the HEG approximation. (Computational Materials Science Group,1998) For a unpolarized system the LDA can be written as ELDAXC=xc(n(r)n(r)dr Where n(r) is the electron density and ?xc is the exchange –correlation energy density. Exc can further be split up as Exc=Ex + Ec where Ex are the exchange functions and Ec is the correlation function.( Computational Materials Science Group,1998) The Perdew-Burke-Ernzerhof (PBE) The interpretation and evaluation of Density functional Theory (DFT) has made the calculation of systems at ground state very effective albeit with several drawbacks. The exchange correlation energy obtained was an approximate value using the LDA method. Further improvement resulted in the introduction of GGA’s or generalized gradient approxi mation to fine tune the LDA. Creating a functional without any empirical parameters the GGA were made to follow certain basic constraints. Since true electron density was actually non-homogenous, it was proposed in 1980 to enhance the density n(r) at a particular point r with inputs regarding the gradient of electron density. To derive an accurate value of the DFT a higher functional satisfying several parameters is ideally chosen. The PBE functional is an ideal functional proposed by Perdew, Burke, Ernzerhof in 1996. Experiments conducted thereafter have proved that the values obtained using these GGA’s were in accordance with those obtained using numerical tests.( Evarestiv R.A, 2007) This PBC functional can be defined as a summation of two derivatives, the XC hole and the energy derivative. This functional is constructed on the premise that the constraints of a particular hole are known and the exchange correlation hole is defined per these constraints. ELSDXC[na, nb]=? d3 rn(r)[?x(n(r))f(?, r) + ?c(rs(r), ?(r))] Where ?=(na-nb)/ (na+nb) is the relative spin polarization and f(?)=1/2[(1+?)4/3 +(1-?)4/3] The exchange energy ?x per electron depends on rs=[3n/4Ð »]1/3 and correlation energy ?c depends on rs and ?.( Evarestiv R.A, 2007) The exchange PBE functional is written as a combination of Ex and Ec. Here the exchange PBE functional EPBEX(n)=?d3rn?x(n)Fx(s) With Fx(s) =1+k-k/(1+ µs2/k) , here k=0.804 and  µ=021951 EPBEC[na, nb]=? d3rn[?C(rs,?)+ H(rs,?,t] where H=? ?3 ln

Systems and Cultural Investigation Essay Example | Topics and Well Written Essays - 1250 words

Systems and Cultural Investigation - Essay Example This paper seeks to analyze the cultural systems that exist in healthcare organizations The term system is a set of interrelated, interacting or interdependent elements that may be used to work together in a certain work environment to perform a particular task that is required by the systems aim. Systems can be improved all the time but before it is improved one must consider knowing how its products are created, the reasons why they are created and how they can be improved. Many systems work under some set of principles so as to help us understand how they behave, for example, the whole system may have one or more of the defining functions. Each part of the system can affect the characters and behaviors of the whole system. Also, it is equally important to note that behaviors and properties of just one part of the system can be very dependent on the behavior of the other parts of the system. Each part of the system may necessarily but may be insufficient to operate alone so as to carry out fully the defining role of the whole system. Healthcare system is often very cumbersome and opaque to their users including patients, nurses, and even the physicians. It best described as complex adaptive systems because they are collections of the individuals who are very free to act in various ways that are unpredictable. The boundaries of the organization can be very fuzzy since membership changes and providers of the services can simultaneously be members of other sub-systems. Given the complexity of these sub-systems, the action of the individual teams are much interconnected so that the action of one sub-system can change the whole context of the other sub-systems. Microsystem may change over time so that it can respond to the needs of their patients, staff members and the external pressure from the surrounding environment. They try to coexist properly with other