A thorough investigation was conducted for the proof process of Heisenberg’s famous inequality. It is apparent that any particle, no matter a classical or a quantum particle, as long as in wave motion, its dp always has an upper limit and a lower limit, which results in the product of dp and dx has both upper and lower limits. The Heisenberg’s inequality is nothing to do with measurement accuracy but related to energy conservation. A new deduction method for a spinning electron revolving on an orbit around a nucleus was developed based on our recently developed theory of spin vector in motion behaving particle-wave duality. The electron’s motion equation is same as Schrodinger equation while with a different energy constant j which is related to the spin vector’s motion features such as the mass of the object, the spin period and revolution period, the orbit shape and size. The new deduction process of Schrodinger equation will help explain the dilemma of the quantum mechanics.
A thorough investigation was conducted for the proof process of Heisenberg’s famous inequality. It is apparent that any particle, no matter a classical or a quantum particle, as long as in wave motion, its dp always has an upper limit and a lower limit, which results in the product of dp and dx has both upper and lower limits. The Heisenberg’s inequality is nothing to do with measurement accuracy but related to energy conservation. A new deduction method for a spinning electron revolving on an orbit around a nucleus was developed based on our recently developed theory of spin vector in motion behaving particle-wave duality. The electron’s motion equation is same as Schrodinger equation while with a different energy constant j which is related to the spin vector’s motion features such as the mass of the object, the spin period and revolution period, the orbit shape and size. The new deduction process of Schrodinger equation will help explain the dilemma of the quantum mechanics.
After the deduction and comparison of wave motions of classical particles and quantum particles, we prove that there are two restrictions applied to both classical particles and quantum particles. Both restrictions are just to ensure energy conservation principle of the wave motion. The Heisenberg’s famous inequality was nothing to do with the measurements of particle’s position or mentum, the restriction of the inequality is just the lower limit of the wave motion. His uncertainty principle was not correct from both mathematical and physical perspective. Based on the mathematic analysis and logic reasoning process review, we conclude that all the Heisenberg’s uncertainty principle, Born rule and Bohr’s complimentary principle were not correct. Even for a quantum particle, at any time, it must be classically localized instead of non-local. Without the Copenhagen interpretations, the quantum mechanics shall still be considered complete according to EPR’s criteria which are used to verify the completeness of a physics theory. The particle-wave duality of quantum particles comes from their inner features of electric vector(s).
This paper is a small discussion about the uncertainty principle. With the great discoveries and researches made by predecessors, I try to answer some questions within the uncertainty principle. Using the definition of momentum, the momentum in de Broglie wave, the property of cosine function, the Euler’s formula, the basic property of plane wave, the law of derivative, the energy of quantum discovered by Max Planck, the photon energy discovered by Albert Einstein, the energy equation of a system and the Hamiltonian operator, I figure out the Schrodinger equation successfully. With the help of Schrodinger equation, the possibility density of a wave function, the concept of normalization, the average value of position and momentum, the Fourier transform, the integration by parts and the limit of normalized wave functions, I find the position operator and the momentum operator. Then using some knowledge of the standard deviation and the variance, the concept of inner product of vectors, some property of Dirac symbol, the law of calculation of complex number and the law of operator calculation, I obtain the general uncertainty relationship of abstract mathematical quantities. According to the general relationship, I get the inequality of uncertainty principle, and discuss the specific relationship between the position and the momentum. After getting the inequality, I use Heisenberg’s experiment of measuring an electron by using the γ ray to hit the electron to explain why we cannot measure the position and the momentum simultaneously. Based on Heisenberg’s experiment, I give my own explanation by discussing the earth and a spacecraft. Transforming the perspective, we can easily see how the accuracies of position and momentum change. In addition, I attempt to figure out why the uncertainty exists. However, I can only explain it by discussing the time and frequency in mathematical method and have no idea to work it out in a pure physics approach.
This article establishes the proof of the Schrödinger equation for numerous quantum systems, utilizing Heisenberg's uncertainty principle. The Fourier transform connects functions in the time and frequency domains, resulting in the mathematical inequality that is the foundation of the uncertainty principle. In the part of Methods and Theory, the article derives the uncertainty principle through Fourier transforms by defining the mean and variance of angular frequency and time, and subsequently expanding the integral. This establishes the fundamental connection between time and frequency domains, illustrating the constraints imposed by quantum mechanics. In the part of Results and Application, the article applies the uncertainty principle to derive the Schrödinger equation under different conditions: free particle, particle in a box, harmonic oscillator, and hydrogen atom. For each case, the article assumes wave function solutions, uses the uncertainty in position and momentum to estimate kinetic and potential energies, and shows that the total energy matches the ground state energy derived from the Schrödinger equation. The results highlight the critical role of Heisenberg's uncertainty principle in understanding key aspects of quantum mechanics, providing a unified framework for these diverse systems.
The results of Bohr model can be used to explain the motion of macroscopic objects or big objects (like orbiting planets and sun, falling stone etc.). These macroscopic objects have essentially a particle nature and Newtonian laws of motion can be applied on them. But it fails when applied to explain the motion of microscopic objects or small objects (like electrons, atoms, molecules etc.). This is because: According to Bohr model, an orbit is a well-defined path and this path can completely be defined only if both the position and velocity of the electron are known exactly at the same time. But this is not possible according to the Heisenberg’s uncertainty principle. Thus, Bohr model contradicts the Heisenberg’s uncertainty principle . According to Bohr model, an electron is regarded as a charged particle moving in well-defined circular orbits concentric about the nucleus. The wave character of the electron is not considered. Thus, Bohr model ignores the de-Broglie dual nature of matter .
The results of Bohr model can be used to explain the motion of macroscopic objects or big objects (like orbiting planets and sun, falling stone etc.). These macroscopic objects have essentially a particle nature and Newtonian laws of motion can be applied on them. But it fails when applied to explain the motion of microscopic objects or small objects (like electrons, atoms, molecules etc.). This is because: According to Bohr model, an orbit is a well-defined path and this path can completely be defined only if both the position and velocity of the electron are known exactly at the same time. But this is not possible according to the Heisenberg’s uncertainty principle. Thus, Bohr model contradicts the Heisenberg’s uncertainty principle . According to Bohr model, an electron is regarded as a charged particle moving in well-defined circular orbits concentric about the nucleus. The wave character of the electron is not considered. Thus, Bohr model ignores the de-Broglie dual nature of matter .
The principle of uncertainty is one of the essential principles of quantum mechanics as it outlines that there is a reflective limit to the measurement of microscopic particle motion. However it is impossible to measure at once and accurately both the position and momentum data of any microscopic particle no matter what means are used to do so. This paper starts by discussing the notion and mathematical derivation of the uncertainty principle as put forth by Heisenberg explaining the physical relevance of the principle. It introduces the natural uncertainty the principle introduces to the dynamics of particles in the microscopic world, and the significant part it plays in the theory of quantum mechanics. The article overviews the explanations of the principle on phenomena including atomic stability and scanning tunneling microscopes, and the interference of measurement actions on the states of particles and the shortcomings of measurement precision. According to the wave-particle duality of quantum mechanics, this article gives a required theoretical basis of microscopic phenomena. Likewise, the use of the research theory on the uncertainty principle by distinguished scholars in the physics fraternity helps the readers in achieving the knowledge in related subjects more easily.