Search results
Results from the WOW.Com Content Network
The wave function of an initially very localized free particle. In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common symbols for a wave function are the Greek letters ψ and Ψ (lower-case and capital psi, respectively). Wave functions are complex ...
More precisely, the Hartle-Hawking state is a hypothetical vector in the Hilbert space of a theory of quantum gravity that describes the wave function of the universe.. It is a functional of the metric tensor defined at a (D − 1)-dimensional compact surface, the universe, where D is the spacetime dimension.
Instead, the wave function must satisfy more complicated mathematical boundary conditions as it is nonzero in regions outside the well. Another related problem is that of the rectangular potential barrier , which furnishes a model for the quantum tunneling effect that plays an important role in the performance of modern technologies such as ...
Functions of this form are known as Bloch functions or Bloch states, and serve as a suitable basis for the wave functions or states of electrons in crystalline solids. The description of electrons in terms of Bloch functions, termed Bloch electrons (or less often Bloch Waves ), underlies the concept of electronic band structures .
The term "wave function" is typically used for a different mathematical representation of the quantum state, one that uses spatial coordinates also called the "position representation". [8]: 324 When the wave function representation is used, the "reduction" is called "wave function collapse".
The condition m=0 is ruled out because = everywhere, meaning that the particle is not in the potential at all. Negative integers are also ruled out since they can easily be absorbed in the normalization condition. We then normalize the wave function, yielding a result where =. The normalized wave function is
The concept of universal wavefunction was introduced by Hugh Everett in his 1956 PhD thesis draft The Theory of the Universal Wave Function. [8] It later received investigation from James Hartle and Stephen Hawking [9] who derived the Hartle–Hawking solution to the Wheeler–deWitt equation to explain the initial conditions of the Big Bang ...
Then solve the differential equation representing this eigenvalue problem in the coordinate basis, for the wave function | = (), using a spectral method. It turns out that there is a family of solutions. In this basis, they amount to Hermite functions, [6] [7] =!