On the Experimental Verification of the Wheeler–DeWitt Equation

1997 ◽  
Vol 12 (28) ◽  
pp. 2057-2064 ◽  
Author(s):  
M. D. Pollock
Keyword(s):  
Wave Function ◽  
Schrödinger Equation ◽  
Cosmological Constant ◽  
Experimental Verification ◽  
Ground State ◽  
Schrodinger Equation ◽  
Approximation Formula ◽  
Neutron Interferometry ◽  
Low Energies ◽  
The Universe

The Wheeler–DeWitt equation ℋΨ=0 for the wave function of the Universe Ψ can be written, in the Friedmann space–time (mini-superspace approximation) [Formula: see text], as the Schrödinger equation [Formula: see text], where ξ≡ dα/dt. The meaning of the pseudo-Hamiltonian [Formula: see text], which reduces to the potential V at low energies, is discussed both classically and quantum theoretically, this equation gives rise to a local gravitational Schrödinger equation which has been verified in the neutron interferometry experiment of Colella et al. By demanding the existence of a global ground state with nonvanishing probability density ΨΨ* for which V=0 (implying the vanishing of the cosmological constant), we argue that this experiment also constitutes evidence for the whole quantization procedure.

On the Vanishing of the Cosmological Vacuum Energy

1997 ◽  
Vol 12 (16) ◽  
pp. 1127-1130 ◽  
Author(s):  
M. D. Pollock
Keyword(s):  
Wave Function ◽  
Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Vacuum Energy ◽  
Ground State Solution ◽  
Space Time ◽  
State Solution ◽  
Superstring Theory ◽  
The Universe

By demanding the existence of a globally invariant ground-state solution of the Wheeler–De Witt equation (Schrödinger equation) for the wave function of the Universe Ψ, obtained from the heterotic superstring theory, in the four-dimensional Friedmann space-time, we prove that the cosmological vacuum energy has to be zero.

STUDY OF THE EXCITED STATE OF DOUBLE-Λ HYPERNUCLEI BY HYPERSPHERICAL SUPERSYMMETRIC APPROACH

2001 ◽  
Vol 10 (02) ◽  
pp. 107-127 ◽  
Author(s):  
MD. ABDUL KHAN ◽  
TAPAN KUMAR DAS ◽  
BARNALI CHAKRABARTI
Keyword(s):  
Wave Function ◽  
Excited State ◽  
Schrödinger Equation ◽  
Ground State Energy ◽  
Ground State ◽  
Schrodinger Equation ◽  
State Energy ◽  
First Excited State ◽  
Three Body ◽  
Partner Potential

Hyperspherical harmonics expansion (HHE) method has been applied to study the structure and ΛΛ dynamics for the ground and first excited states of low and medium mass double-Λ hypernuclei in the framework of core+Λ+Λ three-body model. The ΛΛ potential is chosen phenomenologically while core-Λ potential is obtained by folding the phenomenological Λ N interaction into the density distribution of the core. The parameters of this effective Λ N potential is obtained by the condition that they reproduce the experimental (or empirical) data for core-Λ subsystem. The three-body (core+Λ+Λ) Schrödinger equation is solved by hyperspherical adiabatic approximation (HAA) to get the ground state energy and wave function. This ground state energy and wave function are used to construct a partner potential. The three-body Schrödinger equation is solved once again for this partner potential. According to supersymmetric quantum mechanics, the ground state energy of this potential is exactly the same as that of the first excited state of the potential used in the first step. In addition to the two-Λ separation energy for the ground and first excited state, some geometrical quantities for the ground state of double-Λ hypernuclei [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] are computed. These include the ΛΛ bond energy and various r.m.s. radii.

Solusi Persamaan Schrödinger Berbasis Panjang Minimal untuk Potensial Coulomb Termodifikasi

2018 ◽  
Vol 2 (2) ◽  
pp. 43-47
Author(s):  
A. Suparmi, C. Cari, Ina Nurhidayati
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
Minimal Length ◽  
Energy Spectra ◽  
Atomic Particle ◽  
Approximate Analytical Solutions ◽  
Radial Schrödinger Equation

Abstrak – Persamaan Schrödinger adalah salah satu topik penelitian yang yang paling sering diteliti dalam mekanika kuantum. Pada jurnal ini persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Fungsi gelombang dan spektrum energi yang dihasilkan menunjukkan kharakteristik atau tingkah laku dari partikel sub atom. Dengan menggunakan metode pendekatan hipergeometri, diperoleh solusi analitis untuk bagian radial persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Hasil yang diperoleh menunjukkan terjadi peningkatan energi yang sebanding dengan meningkatnya parameter panjang minimal dan parameter potensial Coulomb Termodifikasi. Kata kunci: persamaan Schrödinger, panjang minimal, fungsi gelombang, energi, potensial Coulomb Termodifikasi Abstract – The Schrödinger equation is the most popular topic research at quantum mechanics. The  Schrödinger equation based on the concept of minimal length formalism has been obtained for modified Coulomb potential. The wave function and energy spectra were used to describe the characteristic of sub-atomic particle. By using hypergeometry method, we obtained the approximate analytical solutions of the radial Schrödinger equation based on the concept of minimal length formalism for the modified Coulomb potential. The wave function and energy spectra was solved. The result showed that the value of energy increased by the increasing both of minimal length parameter and the potential parameter. Key words: Schrödinger equation, minimal length formalism (MLF), wave function, energy spectra, Modified Coulomb potential

Existence of a Ground State Solution for a Quasilinear Schrödinger Equation

2014 ◽  
Vol 14 (4) ◽  
Author(s):  
Xiang-dong Fang ◽  
Zhi-qing Han
Keyword(s):  
Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Ground State Solution ◽  
State Solution ◽  
Quasilinear Schrödinger Equation

AbstractIn this paper we are concerned with the quasilinear Schrödinger equation−Δu + V(x)u − Δ(uwhere N ≥ 3, 4 < p < 4N/(N − 2), and V(x) and q(x) go to some positive limits V

Ground state solution for the Schrödinger equation with Hardy potential and critical Sobolev exponent

2021 ◽  
pp. 1-19
Author(s):  
Jing Zhang ◽  
Lin Li
Keyword(s):  
Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Critical Sobolev Exponent ◽  
Ground State Solution ◽  
Nehari Manifold ◽  
State Solution ◽  
Hardy Potential ◽  
Asymptotically Periodic ◽  
Sobolev Exponent

In this paper, we consider the following Schrödinger equation (0.1) − Δ u − μ u | x | 2 + V ( x ) u = K ( x ) | u | 2 ∗ − 2 u + f ( x , u ) , x ∈ R N , u ∈ H 1 ( R N ) , where N ⩾ 4, 0 ⩽ μ < μ ‾, μ ‾ = ( N − 2 ) 2 4 , V is periodic in x, K and f are asymptotically periodic in x, we take advantage of the generalized Nehari manifold approach developed by Szulkin and Weth to look for the ground state solution of (0.1).

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