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Quantum control

Sculpting a wavepacket

Nature volume 397, pages 207–208 (1999)Cite this article

Classical mechanics governs the motion of macroscopic objects; for example, the state and future motion of a tennis ball is completely determined by its position and momentum at a given time. In contrast, quantum mechanics is needed to describe the motion of microscopic objects, such as an electron in an atom. Heisenberg's uncertainty principle forbids assigning both a well-defined position and momentum to the electron. So, to determine completely the state of this quantum mechanical system, we need a whole distribution of position and momentum values for the electron (that is, the Wigner function).

Another way of expressing the state of a quantum mechanical system is the wavefunction, introduced in 1926 by Erwin Schrödinger. This quantity is a function of either position or momentum, and can take on complex values, having both real and imaginary parts. In the early days of quantum mechanics the physical interpretation of the wavefunction was subject to heated debate, and Schrödinger originally argued that only the real part of this quantity had physical significance. However, Max Born pointed out that only the absolute value squared of the wavefunction is directly experimentally accessible and corresponds to the probability of finding the position or momentum of a particle. (These historical discussions are summarized in ref. 2.) Since we can always represent a complex number by its amplitude and phase, this implies that only the amplitude can be measured directly. The phase is also needed to uniquely describe the quantum state, but how does one find this phase experimentally?

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Figure 1: Sculpting an electronic wavefunction in an atom as described by Weinacht et al.4

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Authors and Affiliations

  1. The Abteilung fr Quantenphysik, Universitt Ulm, Albert Einstein Allee 11, D-89069, Ulm, Germany

    Wolfgang P. Schleich

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  1. Wolfgang P. Schleich
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Schleich, W. Sculpting a wavepacket. Nature 397, 207–208 (1999). https://doi.org/10.1038/16583

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