Quantum‐Mechanical Transition Probabilities for Atom–Atomic‐Oscillator Collisions with Morse Potential Interaction

1971 ◽  
Vol 54 (11) ◽  
pp. 4626-4630 ◽  
Author(s):  
D. J. Diestler ◽  
P. Feuer
Keyword(s):  
Morse Potential ◽  
Transition Probabilities ◽  
Potential Interaction ◽  
Quantum Mechanical ◽  
Mechanical Transition

scholarly journals Quantum Probability's Algebraic Origin

2020 ◽  
Author(s):  
Gerd Niestegge
Keyword(s):  
Transition Probabilities ◽  
Transition Probability ◽  
Wave Functions ◽  
Quantum Mechanical ◽  
Statistical Interpretation ◽  
Quantum Probabilities ◽  
Mechanical Transition ◽  
Definition Of ◽  
Different Origins ◽  
Quantum Indeterminacy

Max Born's statistical interpretation made probabilities play a major role in quantum theory. Here we show that these quantum probabilities and the classical probabilities have very different origins. While the lat- ter always result from an assumed probability measure, the first include transition probabilities with a purely algebraic origin. Moreover, the gen- eral definition of transition probability introduced here comprises not only the well-known quantum mechanical transition probabilities between pure states or wave functions, but further novel cases. A transition probability that differs from 0 and 1 manifests the typical quantum indeterminacy in a similar way as Heisenberg's and others' un- certainty relations and, furthermore, rules out deterministic states in the same way as the Bell-Kochen-Specker theorem. However, the transition probability defined here achieves a lot more beyond that: it demonstrates that the algebraic structure of the Hilbert space quantum logic dictates the precise values of certain probabilities and it provides an unexpected access to these quantum probabilities that does not rely on states or wave functions.

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