Quantum mechanics is a branch of mechanics that incorporates physics concepts associated with uncertainty principles, quantization of energy, correspondence, and wave-particle duality to provide a mathematical description of interaction and motion of particles. Scientists develop new theories and hypotheses under the same mathematical umbrella that unites all the scientific concepts by unifying quantum theory and the general theory of relativity. The general umbrella of physics contains topics that deal with behavior of light and matter at the atomic and subatomic scale, which includes interaction between particles, as well as their interplay with electromagnetic radiation, such as gamma rays and X-rays. The chosen topic under the general umbrella of physics that explains quantum mechanics is the physics of waves. It includes fundamental wave equations that aid in explanation of quantum mechanics concepts and behaviors. Quantum mechanics equations become derived through checking their associations with physics of waves equations, and then, applying physics of waves equations to develop the new ones, solving the problems in quantum mechanics. Physics of waves is suitable for explanation of quantum mechanics because it introduces Heisenberg uncertainty principle and wave-particle duality concepts in high school physics.
The Relationship Physics of Waves Slit Diffraction Experiment with Quantum Mechanics
High school concepts of interference and diffraction play the significant role in explaining quantum mechanics concepts. Slit diffraction experiment forms the basic foundation for this branch of physics. The experimental data shows the behavior of waves when they interact with matter. When an incident wave hits an obstacle, the wave becomes diffracted. In the slit diffraction experiment, the wave becomes diffracted, forming circles, each separated by a distance equal to the diameter of the slit. Dimitrova and Weis (2008) state that when the parallel waves leave the slit, they form concentric waves that appear as bright and dark patches (p.137). The experiment is only true when parallel waves hit an obstacle. The key concept that aid in explaining quantum mechanics is the angle of scattering that is caused by diffraction. After diffraction, the waves leaving the slit and deviate by angle. Despite of having underwent diffraction, the wave poses the same phase as the incident wave. The experimentally derived equation used for calculating the diffraction minima is the following: (? /2) sin ? = ? (??2). Therefore, since the experiment can aid in finding scattering angle and minima can be calculated, physics of waves forms the basis of explain wave particle duality and uncertainty concept.
Physics of Waves Explain Quantum Mechanics Concept of Wave-Particle Duality Concept
The topic of physic of waves acts as the cornerstone to introduction and explanation of quantum mechanics. Chang (2010) state that wave-particle duality forms the basis of quantum physics that explains the application of neutron diffraction (p.2). According to Johansson and Milstead (2008), some high school authors get to Heisenberg uncertainty principle in a different way through stating that fundamental uncertainties ascend from the dispersion of matters wave function (p.173). According to Zwiebach (2013), Schrodinger equation, the equation used in high school physics of waves, describes the dimensions of space in terms of wave function from negative infinity to positive infinity (p.1). Physics of waves provides practical explanation of Heisenberg uncertainty principle without overloading students with deep details. Johansson and Milstead (2008) recommend the use of distinct slit diffraction experimentation in high school to exhibit Heisenberg uncertainty principle through presenting that the effect of the principle it is just wave-particle duality cast in a different light (p.173). Physics of waves shows that, when particles go through a slit, they become diffracted, which results in the particles spreading into a maximum and a minimum. According to Johansson and Milstead (2008), this phenomenon should be witnessed after introduction of wave-particle duality (p.174). Quantum mechanics deals with the behavior of particles at the atomic and subatomic scale. High School physics of waves shows that, when a particle containing Broglie wavelength enters a slit, a single slit diffraction patterns becomes observed. Similar to quantum mechanics, when a similar experiment become repeated with photons or any subatomic particle, the results remain the same (Johansson, & Milstead, 2008, p.174). Despite the physics of wave explaining wave-particle duality concept of quantum physics using diffraction through a slit, the concept of Heisenberg uncertainty principle is not clear. A simple explanation from physics of waves explains wave-particle duality.
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Physics of Waves Form Basis of Deriving Quantum Mechanics Equation of Heisenberg Uncertainty Principle
High school physics of waves gives a different approach when explaining Heisenberg uncertainty principle using the slit diffraction experiment. When exploring Heisenberg uncertainty principle in the slit diffraction experiment, the diffraction experiment becomes interpreted as a limit to nature of the probability or how well the position of a particle with a particular momentum and on a specific position can be identified. Chang (2010) state that Feagin and other conducted an analysis of trapped ion realization, using slit Gedanken experiment, which is demonstrated in high school under the physics of waves topic, to quantify the path followed by a photon (p.2). Therefore, for physics of waves to explain Heisenberg uncertainty principle used in quantum mechanics, assumptions become made in the slit diffraction experiment. Since identifying the exact location of a particle within the slit is difficult, losing the information about the particles momentum is necessary to know that it exists within the slit. However, Johansson and Milstead (2008) state that losing this information is against the laws and principles classical physics (p.174). Therefore, instead of losing the value of momentum, it becomes spread within the slit in different directions to show that the particle exists within the slit that aid in providing position likelihood paths. When the concept becomes incorporated in the slit experiment, conclusions can be made that a particle has a higher probability of existing in one position than in the alternative ones. However, since nature does not enable us to locate both the exact position and momentum of the particle, the values become provided using arbitrary precision. Therefore, the concept shown in the physics of waves slit diffraction experiment explains quantum mechanics principle of Heisenberg uncertainty.
Physics of Waves Form Basis of Deriving Quantum Mechanics Equations
High school physics of wave provides equations that serve the basis for derivation of the quantum mechanics uncertainty equations. From the electron experiment in high school physics of waves topic, when electrons move in the x-direction, they always stick near the maximum distribution. From the slit diffraction experiment, minima scattering Angle ? is given by Broglie wavelength, divided by change in the travelled distance. Broglie wavelength is given by Planks constant divided by the momentum of the electron. The difference between the maxima and the minima scattering angle gives the angular uncertainty. There exists a relationship between the momentum of the electron as it leaves the diffraction experiment slit with the angular uncertainty. According to Johansson and Milstead (2008), angular uncertainty is equivalent to the value of the momentum of scattering electrons, leaving the slit in the x-direction, divided by the momentum of the incoming electron before it enters the slit. From the equation, Planks constant gives the product of the likelihoods of uncertainty in momentum and uncertainty in position (Chang, 2010, p.8). Therefore, physics of waves provide fundamental equations and explanations on how quantum mechanics equations become derived. Also, physics of waves proves the Heisenberg uncertainty principle, which suggests that the precise position and momentum of a particle cannot be simultaneously identified.
Physics of Waves Explain How Quantum Mechanics Make Its Experiment More Accurate
Physics of waves provides concepts that aid in making quantum mechanics explanations more precise. Conferring to high school slit diffraction experiment, for diffraction to occur, the slit must be smaller than the wavelength of the incoming wave. Therefore, when this high school concept is not addressed, when conducting uncertainty experiments in quantum mechanics, the expected results are not achieved by error. Consequently, the accuracy of uncertainty experiment in quantum mechanics depends on the size of the slit and wavelength. Johansson and Milstead (2008) state that high accuracy during investigation of Heisenberg uncertainty principle requires a small slit and a high-speed wave. A wave with a high speed in physics of waves refers to a wave with high frequency and small wavelength. Also, a high frequency wave has high energy. Therefore, according to physics of waves, the most preferred electromagnetic waves for the case, when the size of the slit is small, include X-rays and gamma rays. Therefore, physics of waves explains, why certain parameters become chosen, when conducting quantum mechanics experiments.
Physics of Waves Form Basis of Deriving Additional Quantum Mechanics Equations from Already Existing Equations
Physics of waves explains advancement in the equations used in quantum mechanics. The questions used in the physics of waves form the start point of advancing Heisenberg uncertainty principle from momentum and position to time and energy uncertainty. From high school physics of waves, energy is given as the product of the speed of light squared and mass. When the equation become incorporated in Heisenberg uncertainty principle, uncertainty in energy becomes equivalent to uncertainty in mass multiplied by the speed of light squared (Kolesov et al. 2009). When Heisenberg uncertainty principle become compared to energy-time uncertainty, the product of the uncertainty in position and momentum is equivalent to the product of uncertainty of energy and time. According to Johansson and Milstead (2008), the relationship between the two equations that became derived based on the fundamentals of physics of waves are used in explaining quantum mechanics phenomena, such as radioactivity (p.176). Therefore, physics of waves aids in explaining the applications of quantum mechanics.
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The general umbrella of physics contains topics that provide similar concepts in physics. Therefore, physics of waves explains concepts and equations used in quantum mechanics. The Physics of waves explains the two major theories used in quantum mechanics, which are Heisenberg uncertainty principle and wave-particle duality. High school experiment of slit wave diffraction provides equation used in calculating scattering angle and diffraction minima, (? /2) sin ? = ? (??2), that forms the basis for deriving Heisenberg uncertainty equation. Moreover, deriving the additional quantum mechanics equations is also based on the main concepts and principles in physics of waves. Deriving energy-time uncertainty equation applies the physics of wave equation, which states that energy of a wave is the product of the square of the speed of light and the mass. Physics of waves provide explanations on how quantum mechanics concepts explain measures to guarantee precise results regarding interaction and behaviors of matter. This topic shows that reducing the size of slit in interference experiment results in more precise results. In quantum mechanics, the concept becomes explained in terms of applying high energy waves, which is defined as a wave with high frequency in terms of physics of waves. In addition, physics of waves explain high-energy waves as waves with short wavelengths. This concept is the start point explanation of quantum mechanics in high school and makes it the same important under the general umbrella of quantum physics. Therefore, physics of waves explains wave-particle duality and Heisenberg uncertainty principle, which are among the main concepts in quantum mechanics.
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