Quantum mechanics without probability amplitudes

Y. Kurihara, Nhi My Uyen Quach

We discuss reasons why a probability amplitude, which becomes a probability density after squaring, is considered as one of the most basic ingredients of quantum mechanics. First, the Heisenberg/Schrödinger equation, an equation of motion in quantum mechanics, describes a time evolution of the probability amplitude rather than of a probability density. There may be reasons why dynamics of a physical system are described by amplitude. In order to investigate one role of the probability amplitude in quantum mechanics, specialized codeword-transfer experiments are designed using classical information theory. Within this context, quantum mechanics based on probability amplitude provides the following: i) a minimum error of the codeword transfer; ii) this error is independent of coding parameters; and iii) nontrivial and nonlocal correlation can be realized. These are considered essential advantages of the probability amplitude over the probability density.

Peter Mittelstaedt

Bassano Vacchini

Y. Kurihara, Nhi My Uyen Quach

We discuss reasons why a probability amplitude, which becomes a probability density after squaring, is considered as one of the most basic ingredients of quantum mechanics. First, the Heisenberg/Schrodinger equation, an equation of motion in quantum mechanics, describes a time evolution of the probability amplitude rather than of a probability density. There may be reasons why dynamics of a physical system are described by amplitude. In order to investigate one role of the probability amplitude in quantum mechanics, specialized codeword-transfer experiments are designed using classical information theory. Within this context, quantum mechanics based on probability amplitude provides the following: i) a minimum error of the codeword transfer; ii) this error is independent of coding parameters; and iii) nontrivial and nonlocal correlation can be realized. These are considered essential advantages of the probability amplitude over the probability density.

Lipo Wang, Robert F. O’Connell

F. J. Duarte

Quantum mechanics runs on probability amplitudes. Probability amplitudes must accurately describe the physics prior to calculating the quantum probability. Symbolical probability amplitudes are mathematically represented by complex wave functions. Many physicists in the field don’t even mention the words probability amplitude and prefer to refer to wave function, or state, instead. When they do that they miss out on the subtleties of the physics at hand. In this brief chapter we emphasize probability amplitudes à la Dirac since that is the way Feynman and Ward preferred to describe quantum mechanics. The Dirac notation is also ideally suited to describe quantum interference and quantum entanglement.