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Homogeneity of Space-time Implies the Free Schrodinger Equation
Shan, Gao
Source PublicationNeuroQuantology
AbstractThe free Schrodinger equation is shown to be a consequence of space-time homogeneity in the non-relativistic domain. First, we show that space-time translation invariance of natural laws, which is a conseqiuence of space-time homogeneity, entails that the state of a free particle with definite momentum and energy assumes the plane wave form when the time evolution of the state is linear. Next, we show that the conservation of energy and momentum, which is a consequence of space-time translation invariance, may further determine the energy-momentum relation In the non-relativistic domain. These results then lead to the free Schrodinger equation naturally. The new integrated analysis may help understand the origin of the wave equations in quantum theory.
KeywordSchrodinger Equation Wave Equations Space-time Homogeneity Space-time Translation Invariance Conservation Of Energy And Momentum
WOS HeadingsScience & Technology ; Life Sciences & Biomedicine
Indexed BySCI
WOS Research AreaNeurosciences & Neurology
WOS SubjectNeurosciences
WOS IDWOS:000349007800004
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Document Type期刊论文
AffiliationChinese Acad Sci, Inst Hist Nat Sci, Beijing 100864, Peoples R China
Recommended Citation
GB/T 7714
Shan, Gao. Homogeneity of Space-time Implies the Free Schrodinger Equation[J]. NeuroQuantology,2014,12(4):366-371.
APA Shan, Gao.(2014).Homogeneity of Space-time Implies the Free Schrodinger Equation.NeuroQuantology,12(4),366-371.
MLA Shan, Gao."Homogeneity of Space-time Implies the Free Schrodinger Equation".NeuroQuantology 12.4(2014):366-371.
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