Quantum 2025 – scientific programme

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FRI: Friday Contributed Sessions

FRI 4: Foundational / Mathematical Aspects – Alternative Views

FRI 4.2: Talk

Friday, September 12, 2025, 11:00–11:15, ZHG004

On Schrödinger’s requirements for space functions — •Dieter Suisky — Berlin (suisky5@aol.com)

It will be demonstrated that the wave function and the energy of the ground state of a quantum mechanical system can be derived from the requirements which had been posed by Schrödinger in the First Communication in 1926: In order to substitute the traditional quantum conditions Schrödinger looked for real, single-valued in the whole configuration space, finite and twice continuously differentiable functions. From these requirements alone and the theorem of Rolle it follows that there is such function which (1) is symmetric and zero in the end points, (2) has one maximum and two turning points, (3) the position of the maximum is at x =0. Furthermore, a differential equation of 1st order can be established from which the wave function of the ground state can be calculated. The coordinates of the turning points can be obtained by the differential equation of 2nd order which follows straightforwardly from the previously derived differential equation of 1st order if the condition for all turning points of the twice differentiable space function f(x) is taken into account. Moreover, the energy value of the lowest state can be calculated too and is different from zero, E > 0, which is typical for the quantum mechanical systems. The procedure fits for the quantum mechanical harmonic oscillator. The differential equation of 2nd order is nothing else the well-known Schrödinger equation, which is now already obtained from a differential equation of 1st order. The analysis of the relations between differential equations of different orders can be traced back to Euler.