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.

Oxidation of Aqueous Thiosulfate Solutions by Pulsed Corona Discharge

The aim of this Master’s thesis focused on the oxidation of sodium thiosulfate using non thermal plasma technology as an advance oxidation process (AOP). By using this technology we can degrade certain toxic chemical compounds present in mining wastewaters as pollutants. Different concentrations of thiosulfate and pulse frequencies were used in the PCD experiments and the results in terms of various delivered energies (kWh/m3) and degradation kinetics were compared. Pulsed corona discharge is an energy efficient process compared to other oxidation processes using for the treatment of waste water pollutants. Due to its simplicity and low energy costs make it attractive in the field of waste water treatment processes. This technology of wastewater treatment has been tested mainly on pilot scale level and in future the attempts are to be focus on PCD investigations on larger process scale. In this research work of oxidation of thiosulfate using pulsed corona discharge, the main aim of this research was to study degradation of a studied toxic and not environmental friendly chemical compound. The focus of this research was to study the waste waters coming from the gold mines containing leachate compound thiosulfate. Literature review contained also gold leaching process when cyanide is used as the leachate. Another objective of this work was to compare PCD process with other processes based on their energy efficiencies. In the experimental part two concentrations of sodium thiosulfate, 1000ppm and 400ppm, were used. Two pulse generator frequencies of 833 and 200 pulses per second (pps) were used. The chemical analyses of the samples taken during semi-batch PCD oxidation process were analyzed by ion chromatographic (IC). It is observed after the analyses that among different frequencies and concentrations, the most suitable ones for the process is 200pps and 1000ppm respectively because the pollutants present in the waste water has more time to react with the OH radicals which are the oxidants and the process is energy efficient compared to other frequencies.

Solutions to water problems in the bottom of the pyramid market

Solving the water crisis in the developing world is a critical issue. Four billion people in the globe, so called the Base of the Pyramid (BoP) population suffer from inadequate access to safe drinking water, while millions die daily from waterborne diseases and lack of clean water. The BoP people desperately need to obtain a satisfactory access to safe water sources. In order to address the issue, this research has been carried out. To provide holistic consideration to the matter, comprehensive exploration of various causes of the water crisis and its impacts in developing countries were discussed. Then, various viable and relevant solutions to the problem have been thoroughly scrutinized, including scientific, rational, practical and speculative approaches, examination of existing methods, technologies and products at the BoP water market. The role of clean water to the sustainable development was specifically featured. The paper also has studied social and economic factors, actors and circumstances which affect the market development of clean water technologies in the BoP. Possibilities and potentials of successful business between foreign water enterprises and BoP consumers were considered, while primary obstacles are deliberated on, with suggestion of the ways to tackle them. Technologies and products which are needed by the poor must be affordable, sustainable and of an appropriate quality. The crucial question of technology transfer was soundly discussed with pointing out main hindrances on the way of its implementation between the developed and developing world. The means to overcome these barriers were properly observed as well. To explore to some extent the possibility and feasibility of technology transfer from Finland to the BoP sector, 3 case study analyses have been implemented. Personal discussions in form of interviews were conducted at Kemira, Outotec and Fenno Water, Finnish water treatment and supply enterprises. The results of the interviews shed light on the specific practical matters, actual obstacles and potential solutions of the technology transfer from Finland to low-income countries.

Distribution of Smart Solutions for External Lighting in Switzerland - Case C2 Smartlight Ltd.

Establishing of export operations is the key to the competitiveness for all producing companies in high-tech industry. Distribution partnerships between exporting producer and local distributors of relevant foreign market are utilized by SMEs to gain cost-efficiency of operation. The purpose of this study was to investigate the Swiss market of outdoor lighting solutions and propose distribution channels for the case of company C2 SmartLight Ltd. The literature framework consists of three main parts: description of distribution channels for business products, the selection process of the distributor and management of the distributors. The empirical part of this study composed of the observation of Swiss lighting market, highlighting key customers, trends of energy efficiency and key industry players of the lighting market. The aim was to identify potential distribution channels, which reach the target customer groups and identify the market opportunity. Secondly, the data was collected through semi-structured phone interviews. The company, which operates in outdoor lighting business and has an established distributor in Switzerland, was interviewed and used as a benchmark. As a result of this research the market opportunity for distribution of C2 SmartLight products was identified based on potential customers and market need. C2 SmartLight Ltd. should establish a connection with wholesalers that distribute easy to handle and store electrical equipment. The results of this study can be used by other SME companies, operating in a similar field of economy, for selection of distributors.