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1-8: Summary of Part 1

Let us summarize what we have learned in Part 1.
(1) Schroedinger introduced a wave equation which the de Broglie wave accompanying the motion of a substance particle should satisfy. It was called the Schroedinger equation and became the fundamental equation of quantum mechanics.
(2) Heisenberg thought that, in the microscopic world, the position and momentum coordinates, q and p , are not such ordinary variables as those in the classical mechanics but that they are matrices. Thereby he proposed the matrix mechanics. It was clarified that these two types of mechanics, Schroedinger's wave mechanics and Heisenberg's matrix mechanics, are equivalent to each other.
(3) It had been clarified in the microscopic world that it is in principle impossible to measure the position and momentum of a particle more precisely than the limitations prescribed by Heisenberg's uncertainty principle. Accordingly, it was made clear that, in the microscopic world, the concept of "orbit" of a particle, which can be described by a curved "line", must be abandoned.
(4) The probability interpretation of the wave function was proposed. It claims that the square of the absolute value of the wave function denotes the probability density that the particle will be found. It was elucidated that the tunnel effect, based on this idea, can explain the alpha decay of atomic nuclei. This was one of the strong proofs of the validity of quantum mechanics.

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