The Uses and Significance of Quantum Mechanics in Nanotechnology - Paper Example

Introduction

Nanotechnology is a novel branch of applied science, concerned with fundamental properties of matter at the nano-scale and applying them for the benefit of the society (Baggott, 2009). Quantum mechanics supplants and transcends classical mechanics at the subatomic and atomic levels. It offers the underlying framework for numerous subfields of chemistry, physical and material science. It presents the only approach to comprehending the structural make up of materials, from metals to semiconductors (Mehra & Rechenberg, 2010). The paper reviews the uses and significance of quantum mechanics in nanotechnology. It is argued quantum mechanics has enabled accurate representation of the performance of nanomachines, which was not feasible under classic mechanics. The discipline has provided means for accurately computing ground-state-wave functions and energies and the subsequent modeling of these systems.

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Nanotechnology is the use of Quantum physics and a practical realm of Quantum Theory. The obvious desire of scientists to produce self-contained, light and energy efficient devices to supplant gigantic microelectronic equipment is pegged on the nature of quantum variance. Researchers speculate that solitary molecular sensors can be produced and that advanced neural-oriented networks and memory storage can be achieved with relatively fewer molecules. Quantum hypothesis and mechanics depict the connection between matter and energy on the subatomic and atomic scale. Toward the start of the twentieth century, Maxwell Planck proposed that atoms emit or absorb electromagnetic radiation in quanta, energy bundles. The quantum idea appeared to be illogical to the well-entrenched Newtonian material science. Headways related to quantum mechanics likewise had significant ramifications concerning the philosophical logical contentions in regards to the potentials of nanotechnology.

The study of Max Planck on blackbody radiation and his startling revelation that matter transferred energy through radiation in discrete increments referred to as quanta is the origination quantum mechanics as a discipline. During the time, Max Planck was uncertain of the implication of his discovery, wondering whether nature behaved in such a manner. However, good fit data was acquired from blackbodies through further investigation. It is important to take note if Planck's investigation would have been fruitless, it would have suggested that matter exchange energy with radiation continuously regardless of the frequency, and quantum mechanics would nonexistent today.

Photoelectric Effect

The photoelectric effect depicted a number of features and they are as follows. No electrons are catapulted irrespective of the intensity of radiation unless the incident radiation's frequency surpasses a threshold value. The kinetic energy of the capitulated electrons increments with a recurrence of incident radiation and is autonomous of the power of radiation. Even at relatively lower intensities, electrons are repelled when the threshold frequency is surpassed.

In understanding these observations, Einstein proposed equation 1:

Equation (1)

Where mev2 is the kinetic energy of the propelled electrons and the function of the propellant solid. Einstein recommended that the energy of light, regardless of the frequency, is given by the equation, a thought that he obtained and amplified from the analysis of blackbody radiation by Plank. The equation proposed by of Einstein that effectively explained the data generated from studies on photoelectric effect inferred that the frequency's electromagnetic radiation does not possess energies rather than a distinctive type of energy, and behaves as though it has numerous particles each containing defined level of energy. Particularly, the condition suggested that light, at any given frequency, could not possess energy with non-integral multiples. The light was, for a very long time, thought to exhibit wave-live behavior, but suddenly appeared to show behavior resembling that of a particle. Einstein named these light particles as photons, and it is fascinating to take note of that almost two hundred years prior to the analysis by Einstein, Newton had proposed that light comprised of particles, which he referred to as corpuscles. When experiments demonstrated that light depicted inference and diffraction phenomena, Newton's view of light's particles were deserted and the wave concept of light was reignited. With the analysis by Einstein, the thought of light as particles reemerged and gained wide acceptance. Despite Newton being the initiator of the idea, Einstein took the credit for it by placing a more grounded theoretical footing and effectively expounded on the phenomenon whereas Newton simply recommended the likelihood.

Einstein was likewise irresponsible for the introduction of relativity concept, the general theory of relativity, as well as the special theory of relativity. Einstein was acknowledged for his contributions to the photoelectric effect, a sign maybe of how fundamental quantum mechanics transformed the scientific landscape. Whereas Einstein proposed that light, which had been thought of as waves, could likewise be viewed as particles, Louise de Broglie believed the opposite. He believed that light was composed of particles that could be viewed as waves. Louis de Broglie indicated that the possibility that any particle, moving with a straight momentum, can be viewed as having a wavelength l computed as:

Equation (2)

The probability that particles could be viewed as waves; they were effectively investigated by Gremer and Davisson. These scholars showed that a light emission could diffract. Electrons from a warmed fiber, occurrence on a Ni test, showed diffraction (Sedha, 2010). The diffraction was demonstrated when electrons generated from a sample of Nickel filament was heated.

The theory of Louise de Broglie suggested that even large objects of every day can be viewed as having wavelength connected to them. Utilizing his hypothesis, it is established that in reality such a wavelength can be resolved notwithstanding the size of the object. The only issue is that a wavelength becomes insignificant as the size of the object increases and it would not impact the physical observation and object's interactions. Between Louis, Einstein, and Davison et al, scholars were familiarized with the thoughts that waves could depict particles as behavior and all particles have behavior that mimics waves (Greenberger, Hentschel & Weinert, (2011). Quantum Mechanics introduced inside its frame functions the concept of wave-particle duality. The approach by and by embraced in material science is to regard matter either as particles or as waves altogether in view circumstances. When convenient the description of particles as a matter is accepted and the reverse is true.

Schrodinger Wave Equation

New apparatuses were required to address the quantum mechanics' ideas. The direction of particles in traditional material science, expected to fit within the portrayal of a wave, a necessity that was addressed successfully by Erwin Schrodinger. Quantum mechanics acknowledges the duality of wave-particle by handling the particle's trajectory as a wave, indicated using a wave function ps. The function ps of the wave has the properties of the quantum mechanics framework and is achieved through the solving of the Schrodinger wave equation.

Equation (3)

The wave equation of Schrodinger cannot be derived based on fundamental principles because it is considered basic in itself. It only expresses that the aggregate energy of the system comprises of the kinetic and potential energies of the system. In the investigations involving quantum mechanics, constraints set on the system are typically identified and the wave equation of Schrodinger is solved in accordance with the established limitations (Taketani & Nagasaki, 2011). The function ps subsequently embodies the properties of the subject system. Schrodinger presented the instrument that could be used in the extraction of parameters critical to the comprehension of the system in the premise of quantum mechanics.

The Schrodinger wave condition is anything but difficult to tackle except for a couple of straightforward cases. It can be very convoluted to solve and can call for a given mathematical tool in most cases. The equation shown above is a case of the form it may take, referred to as the time-independent wave equation, with others, take the time-dependent form. The last version conflicts with certain conditions of relativity, indicating that there are other aspects of nature that are yet to be revealed scientifically.

Born Interpretation of Wave Function

Whereas the wave equation postulated by Schrodinger was acknowledged as the basic elements of the quantum mechanics, extensive perplexity won on the noteworthiness of the wave function ps. Max Born interpreted the wave function ps. Considering that ps is the intricate conjugate of ps, Born indicated that |dx| 2 or ps ps*dx, is the likelihood of locating the electron between (x + dx) and x. For a held electron, for instance, ps, the wave function, will end up to have a high value when an atom is closer and will remain zero when it is alone (Vasudeva, 2008). Niels Bohr examined molecular and atomic spectra and endeavored to clarify the discrete form of these spectra. He suggested that electrons circumvented the nucleus in stationary orbits and that the energy discharged when electrons hopped between orbits was a fixed value contingent upon the number of orbits jumped. Whereas the atom's planetary model has not been verified completely, it failed to explain the spectra observed. Schrodinger demonstrated that the outcomes obtained through the wave functions were steady with Niels Bohr's predictions.

As demonstrated before, it is difficult to solve the wave equation proposed by Schrodinger in most cases. By itself, the wave function can end up being exceptionally confounded. When the function is thought of as an aggregate of numerous waves, each estimate of the particle's momentum will bring about a value relating to any of the waves that constitute the wave function.

The idea and its astonishing ramifications were investigated by Heisenberg and prompted his distinguishing proof of the 'Uncertainty Principle'. The principle credited to Heisenberg, adequately expresses that when the particle's location is identified decisively, the determination of its underlying momentum will be imprecise or very difficult. In simplifying the multifaceted nature of the concepts involved, the theory is explained by asserting that the particle's position is definite, and light is shone on the particle for visibility. Subsequently, the force of the molecule changes and we are thus the position is indeterminate at the same time. The issue with the above scenario is that it gives the impression that the uncertainty principle by Heisenberg is simply an experimentation limitation.

Uncertainty Principle

Studies have not reported a reduction in uncertainty with regards to the uncertainty principle by Heisenberg. Such an absence of improvement is an indication that the standard is not among the exploratory constraint. A further developed perspective of the uncertainty is as indicated. Energy and location of a molecule are associated with a Fourier transform and henceforth are alluded to as conjugate factors of each other. It becomes apparent that when Fourier transforms us carried out, the product variability of a single variable and its conjugate, as a result of Fourier transform process, become equivalent to or more than a specific value. For instance, when variables A and B are associated with a Fourier transform and are a representative of the va...