The solutions and tunneling properties for a linear potential and an inverted harmonic oscillator in an infinite well

In this work we look at two different 1-dimensional quantum systems. The potentials for these systems are a linear potential in an infinite well and an inverted harmonic oscillator in an infinite well. We will solve the Schrödinger equation for both of these systems and get the energy eigenvalues and eigenfunctions. The solutions are obtained by using the boundary conditions and numerical methods. The motivation for our study comes from experimental background. For the linear potential we have two different boundary conditions. The first one is the so called normal boundary condition in which the wave function goes to zero on the edge of the well. The second condition is called derivative boundary condition in which the derivative of the wave function goes to zero on the edge of the well. The actual solutions are Airy functions. In the case of the inverted oscillator the solutions are parabolic cylinder functions and they are solved only using the normal boundary condition. Both of the potentials are compared with the particle in a box solutions. We will also present figures and tables from which we can see how the solutions look like. The similarities and differences with the particle in a box solution are also shown visually. The figures and calculations are done using mathematical software. We will also compare the linear potential to a case where the infinite wall is only on the left side. For this case we will also show graphical information of the different properties. With the inverted harmonic oscillator we will take a closer look at the quantum mechanical tunneling. We present some of the history of the quantum tunneling theory, its developers and finally we show the Feynman path integral theory. This theory enables us to get the instanton solutions. The instanton solutions are a way to look at the tunneling properties of the quantum system. The results are compared with the solutions of the double-well potential which is very similar to our case as a quantum system. The solutions are obtained using the same methods which makes the comparison relatively easy. All in all we consider and go through some of the stages of the quantum theory. We also look at the different ways to interpret the theory. We also present the special functions that are needed in our solutions, and look at the properties and different relations to other special functions. It is essential to notice that it is possible to use different mathematical formalisms to get the desired result. The quantum theory has been built for over one hundred years and it has different approaches. Different aspects make it possible to look at different things.

Tuulivoimaliiketoimintaan liittyviä epävarmuustekijöitä

Diplomityön tavoitteena oli selvittää tuulivoimatuotannon epäsymmetrisyyden vaikutuksia liiketoiminnalle. Tarkastelun kohteena oli tuotetun energian sekä tuulivoimatuotannosta maksettavan korvauksen keskinäinen epäsymmetria. Työssä asiaa tarkasteltiin esimerkki tuulivoimalaitoksen avulla. Tarkastelujaksoksi työssä rajattiin ajanjakso 2014 tammikuusta vuoden 2015 kesäkuuhun. Tämän lisäksi työssä perehdyttiin tuotetun sähkön hinnan suojausstrategioihin, tuotannon häviötekijöihin sekä tasesähkön aiheuttamien kustannusten kehitykseen. Työn tulosten perusteella tuulivoimaliiketoiminta tulee kokemaan epävakauden lisääntymistä. Tuulivoimatuotannon epävarmuus johtuu heikosta pitkän aikavälin ennustettavuudesta, joka koostuu aikaisemmin mainituista tuotannon ja sähkön markkinahinnan välisestä epäsymmetrisyydestä. Työssä käsitellään tuulivoimatuotannon ajallista vaihtelua, joka ilmentää hyvin tuulivoimatuotannon perimmäistä olemusta. Työn lopputuloksena saatiin kuvaus tuotantojen ajallisesta jakautuneisuudesta, joiden pohjalta yritys voi suunnitella suojausstrategioita työssä esiteltyjen johdannaistuotteiden avulla. Edellisten loppupäätelmien lisäksi työssä perehdyttiin häviöiden sekä tasesähkökustannusten taloudellisiin vaikutuksiin sekä kehityssuuntiin tulevaisuudessa.

Viologen based electroactive polymers and composites for durable electrochromic systems

Electrochromism, the phenomenon of reversible color change induced by a small electric charge, forms the basis for operation of several devices including mirrors, displays and smart windows. Although, the history of electrochromism dates back to the 19th century, only the last quarter of the 20th century has its considerable scientific and technological impact. The commercial applications of electrochromics (ECs) are rather limited, besides top selling EC anti-glare mirrors by Gentex Corporation and airplane windows by Boeing, which made a huge commercial success and exposed the potential of EC materials for future glass industry. It is evident from their patents that viologens (salts of 4,4ʹ-bipyridilium) were the major active EC component for most of these marketed devices, signifying the motivation of this thesis focusing on EC viologens. Among the family of electrochromes, viologens have been utilized in electrochromic devices (ECDs) for a while, due to its intensely colored radical cation formation induced by applying a small cathodic potential. Viologens can be synthesized as oligomer or in the polymeric form or as functionality to conjugated polymers. In this thesis, polyviologens (PVs) were synthesized starting from cyanopyridinium (CNP) based monomer precursors. Reductive coupling of cross-connected cyano groups yields viologen and polyviologen under successive electropolymerization using for example the cyclic voltammetry (CV) technique. For further development, a polyviologen-graphene composite system was fabricated, focusing at the stability of the PV electrochrome without sacrificing its excellent EC properties. High electrical conductivity, high surface area offered by graphene sheets together with its non-covalent interactions and synergism with PV significantly improved the electrochrome durability in the composite matrix. The work thereby continued in developing a CNP functionalized thiophene derivative and its copolymer for possible utilization of viologen in the copolymer blend. Furthermore, the viologen functionalized thiophene derivative was synthesized and electropolymerized in order to explore enhancement in the EC contrast and overall EC performance. The findings suggest that such electroactive viologen/polyviologen systems and their nanostructured composite films as well as viologen functionalized conjugated polymers, can be potentially applied as an active EC material in future ECDs aiming at durable device performances.