# The mathematical formulations of quantum mechanic

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## The mathematical formulations of quantum mechanic

The mathematical formulations of quantum mechanics are abstract. Similarly, the implications are often non-intuitive in terms of classic physics. The centerpiece of the mathematical system is the wavefunction. The wavefunction is a mathematical function providing information about the probability amplitude of position and momentum of a particle. Mathematical manipulations of the wavefunction usually involve the bra-ket notation, which requires an understanding of complex numbers and linear functionals. The wavefunction treats the object as a quantum harmonic oscillator and the mathematics is akin to that of acoustic resonance. Many of the results of quantum mechanics do not have models that are easily visualized in terms of classical mechanics; for instance, the ground state in the quantum mechanical model is a non-zero energy state that is the lowest permitted energy state of a system, rather than a more traditional system that is thought of as simply being at rest with zero kinetic energy.

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