Solving Schrödinger equation for bipartite hard-core potential by virtue of the entangled state representation

2019 ◽  
Vol 97 (1) ◽  
pp. 82-85
Author(s):  
Hai-jun Yu ◽  
Hong-Yi Fan
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Hard Core ◽  
Quantization Condition ◽  
Entangled State ◽  
Entangled State Representation ◽  
State Representation ◽  
One Dimensional ◽  
Core Potential ◽  
The One

We study the one-dimensional Schrödinger equation for the Hamiltonian involving the bipartite hard-core potential, [Formula: see text]. We select the suitable unitary transformation and employ the entangled state representation |η⟩, η = η1 + iη2, to find the quantization condition for energy E, [Formula: see text] which seems new.

A TWELFTH-ORDER FOUR-STEP FORMULA FOR THE NUMERICAL INTEGRATION OF THE ONE-DIMENSIONAL SCHRÖDINGER EQUATION

2003 ◽  
Vol 14 (08) ◽  
pp. 1087-1105 ◽  
Author(s):  
ZHONGCHENG WANG ◽  
YONGMING DAI
Keyword(s):  
Schrödinger Equation ◽  
Numerical Integration ◽  
Schrodinger Equation ◽  
Numerical Test ◽  
New Method ◽  
Step Method ◽  
One Dimensional ◽  
The Stability ◽  
The One ◽  
Order Four

A new twelfth-order four-step formula containing fourth derivatives for the numerical integration of the one-dimensional Schrödinger equation has been developed. It was found that by adding multi-derivative terms, the stability of a linear multi-step method can be improved and the interval of periodicity of this new method is larger than that of the Numerov's method. The numerical test shows that the new method is superior to the previous lower orders in both accuracy and efficiency and it is specially applied to the problem when an increasing accuracy is requested.

Sign in / Sign up

Export Citation Format

Share Document