![]() This explains the name "wave function", and gives rise to wave–particle duality. The Schrödinger equation determines how wave functions evolve over time, and a wave function behaves qualitatively like other waves, such as water waves or waves on a string, because the Schrödinger equation is mathematically a type of wave equation. The inner product between two wave functions is a measure of the overlap between the corresponding physical states and is used in the foundational probabilistic interpretation of quantum mechanics, the Born rule, relating transition probabilities to inner products. When a system has internal degrees of freedom, the wave function at each point in the continuous degrees of freedom (e.g., a point in space) assigns a complex number for each possible value of the discrete degrees of freedom (e.g., z-component of spin) – these values are often displayed in a column matrix (e.g., a 2 × 1 column vector for a non-relativistic electron with spin 1⁄ 2).Īccording to the superposition principle of quantum mechanics, wave functions can be added together and multiplied by complex numbers to form new wave functions and form a Hilbert space. Some particles, like electrons and photons, have nonzero spin, and the wave function for such particles includes spin as an intrinsic, discrete degree of freedom other discrete variables can also be included, such as isospin. For instance, it may be taken to be a function of all the position coordinates of the particles over position space, or the momenta of all the particles over momentum space the two are related by a Fourier transform. Once such a representation is chosen, the wave function can be derived from the quantum state.įor a given system, the choice of which commuting degrees of freedom to use is not unique, and correspondingly the domain of the wave function is also not unique. The wave function is a function of the degrees of freedom corresponding to some maximal set of commuting observables. The most common symbols for a wave function are the Greek letters ψ and Ψ (lower-case and capital psi, respectively). The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements made on the system can be derived from it. In quantum physics, a wave function is a mathematical description of the quantum state of an isolated quantum system. Panels (G–H) further show two different wave functions that are solutions of the Schrödinger equation but not standing waves. ![]() Panels (C–F) show four different standing-wave solutions of the Schrödinger equation. ![]() Rather, it is represented as a wave here, the vertical axis shows the real part (blue) and imaginary part (red) of the wave function. The quantum process (C–H) has no such trajectory. The classical process (A–B) is represented as the motion of a particle along a trajectory. Comparison of classical and quantum harmonic oscillator conceptions for a single spinless particle. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |