# John von Neumann

### (1903- 1957)

## Child years-

## Older Years

## After college-

*"John von Neumann from Berlin wrote a letter to his professor Lipót Fejér in Budapest (1929)"*

## Von Neumann's Theories

## Game Theory

## Quantam Theory

Quantum theory is the theoretical basis of modern physics that explains the nature and behavior of matter and energy on the atomic and subatomic level. In 1932, in __Mathematical Foundations of Quantum Mechanics__, John von Neumann explained that two fundamentally different processes are going on in quantum mechanics, not at the same time. Process 1 of the quantum theory is a “non-causal process”, in which the measured electron winds up randomly in one of the possible physical states (eigenstates) of the measuring apparatus plus electron. The probability for each eigenstate is given by the square of the coefficients (**c n**) of the increase of the original system state (wave function

**ψ**) in an endless set of wave functions (

**φ)**that represent the eigenfunctions of the measuring apparatus plus electron. According to von Neumann, the particle simply shows up somewhere as a result of a measurement.

Ex. c*n* = < **φ***n* | **ψ** >