Transition probability of particle’s Quantum State Author, Samuel Mulugeta Bantikum University of Gondar, Department of Physics. An alternative name is non-commutative probability theory. Use the Schrödinger Equation and its complex conjugate (We assume is real. Imaginative recreation of quantum forces at work. Imaginary potentials do cause probability not to be conserved.) (Image: Jurik Peter/Shutterstock) Dice and the Theory of Probability. Now we need to plug those equations in. In Quantum Mechanics, we understand this wave-particle duality using (complex) probability amplitudes which satisfy a wave equation. Quantum probability equation: I 7355 which has the correct classical solution of P(r)≈ C √ E−U(r) (2.4) It is also easy to show that any zero of P(r)is of even order so, if the probability is positive at small distances, then it remains non-negative for all r. u(r)is continuous at these zeros and so one can deduce uniquely the form of u(r)from the solution for P(r). The probability to find a particle at a position at some time is the absolute square of the probability amplitude . The intensity of a wave is what’s equal to the probability that the particle will be at that position at that time.. That’s how quantum physics converts issues of momentum and position into probabilities: by using a wave function, whose square tells you the probability density that a particle will occupy a particular position or have a particular momentum. Probability Conservation Equation * Start from the probability and differentiate with respect to time. Finally, this leads to the possibility of quantum theory with other sorts of auxiliary equations instead of Schrodinger's equation, and examples of this are given. Quantum probability theory is a generalization of probability theory in which random variables are not assumed to commute. Abstract This study mainly focused on calculating the transition probability of a particles in a given quantum state based on the idea of quantum jump,since Quantum particles can change their quantum state very quickly. In 1654, a French nobleman, the Chevalier de Méré, noticed something while gambling. If the double-slit experiment encapsulates the essence of quantum mechanics in one basic experiment, Schrödinger’s probability wave equation has been described as its central ingredient, its hallmark feature, its mathematical engine [1]. It developed in the 1970's from an urge to apply probabilistic concepts, such as "independence" , "noise" and "process" , to quantum mechanics. Dice play a significant role in our understanding of probability and its relation to the universe.