Understanding Electronic Wave Functions

Louis C. Green

Hironari Yamada

We all physicist have long been believed that an elementary particle is a wave as well as a particle, but we discuss in this paper that an electron (probably all fermions) is always a particle. Author claim that quantum mechanics (QM) is not such mysterious as Bohr stated that the wave turn to the particle by observation. We can understand QM by natural human sense. The wave nature of electrons is only an appearance or a phenomena but not intrinsic or substantial. An electron is an individual body, which interferes with other individual electrons. Interference is the key word instead of the wave to understand the quantum mechanics. Interference produces the wave nature and the uncertainty. When we determine that an electron is nothing but a particle, we will see the true meaning of wave function and the Schr?dinger’s equation.

Jochen Vogt

Peipei Ge, Yankun Dou, Meng Han +5 more

Electrons detached from atoms by photoionization carry valuable information about light-atom interactions. Characterizing and shaping the electron wave function on its natural timescale is of paramount importance for understanding and controlling ultrafast electron dynamics in atoms, molecules and condensed matter. Here we propose a novel attoclock interferometry to shape and image the electron wave function in atomic photoionization. Using a combination of a strong circularly polarized second harmonic and a weak linearly polarized fundamental field, we spatiotemporally modulate the atomic potential barrier and shape the electron wave functions, which are mapped into a temporal interferometry. By analyzing the two-color phase-resolved and angle-resolved photoelectron interference, we are able to reconstruct the spatiotemporal evolution of the shaping on the amplitude and phase of electron wave function in momentum space within the optical cycle, from which we identify the quantum nature of strong-field ionization and reveal the effect of the spatiotemporal properties of atomic potential on the departing electron. This study provides a new approach for spatiotemporal shaping and imaging of electron wave function in intense light-matter interactions and holds great potential for resolving ultrafast electronic dynamics in molecules, solids, and liquids.

Peter Fulde

Junheng Pan, Shaoran Liu, Bozhou Zhang +2 more

Abstract In Copenhagen’s interpretation, a self-interference mechanism is assumed for a wave function to split and to pass through the slits simultaneously, then recombine and collapse to generate a dot signal on a detector. Its use of a single wave function to describe a whole ensemble without accounting for a particle’s individuality is incomplete. To better understand the single-electron double-slit interference, we use a wave-packet trajectory approach to track each electron’s dynamics and calculate the time-dependent interference intensity. We analyze the self-interference and cross-interference mechanisms to illustrate how an electron’s coherence length affects the self-interference and how it dictates the wave packet overlaps between adjacent electrons for the cross-interference mechanism to be effective. To circumvent a conflicting dilemma between the electron’s indivisibility and its wave-packet split while passing through the slits, we consider an alternate mechanism involving slit-induced quantized momentum. This mechanism preserves the electron’s indivisibility and avoids the illusive split, recombination and mysterious collapse of a single particle’s wave function.