The Hamiltonion for the double well and triple wells can be written in form $H=H_0-x^2+x^4$ and $H=H_0+x^2-x^4+x^6$, repectively. Can anyboody guide which "basis function" can be used to construct the corresponding matrix elements for double and triple wells (which full-fills the BC's).? Please also tell me which method can be used to calculate the matrix elemnents,which may includes number of Gaussian integrals to solve.(Waiting for yours suggestion).+
2026-02-23 09:02:41.1771837361
Double wells and triple wells quantum oscillators
85 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in LINEAR-ALGEBRA
- An underdetermined system derived for rotated coordinate system
- How to prove the following equality with matrix norm?
- Alternate basis for a subspace of $\mathcal P_3(\mathbb R)$?
- Why the derivative of $T(\gamma(s))$ is $T$ if this composition is not a linear transformation?
- Why is necessary ask $F$ to be infinite in order to obtain: $ f(v)=0$ for all $ f\in V^* \implies v=0 $
- I don't understand this $\left(\left[T\right]^B_C\right)^{-1}=\left[T^{-1}\right]^C_B$
- Summation in subsets
- $C=AB-BA$. If $CA=AC$, then $C$ is not invertible.
- Basis of span in $R^4$
- Prove if A is regular skew symmetric, I+A is regular (with obstacles)
Related Questions in MATHEMATICAL-PHYSICS
- Why boundary conditions in Sturm-Liouville problem are homogeneous?
- What is the value of alternating series which I mention below
- Are there special advantages in this representation of sl2?
- Intuition behind quaternion multiplication with zero scalar
- Return probability random walk
- "Good" Linear Combinations of a Perturbed Wave Function
- Yang–Mills theory and mass gap
- Self adjoint operators on incomplete spaces
- Algebraic geometry and algebraic topology used in string theory
- Compute time required to travel given distance with constant acceleration and known initial speed
Related Questions in QUANTUM-MECHANICS
- Is there a book on the purely mathematical version of perturbation theory?
- Matrix differential equation and matrix exponential
- "Good" Linear Combinations of a Perturbed Wave Function
- Necessary condition for Hermician lin operators
- What is a symplectic form of the rotation group SO(n)
- Why is $\textbf{J}$ called angular momentum?(Quantum)
- How does the quantumstate evolve?
- Differential equation $au''(x)+b\frac{u(x)}{x}+Eu=0$
- How to model this system of $^{238}\,U$ atoms?
- Discrete spectra of generators of compact Lie group
Related Questions in OSCILLATORY-INTEGRAL
- Problem regarding to solve "6 nonlinear dynamic system of first order differential equation" analytically ( approximated )
- Non-vanishing of K-Bessel function
- How to disprove an equality involving a double integral
- Is $\int_{A_t} \frac{1}{|x_j|^{p}}\, dx \leq \sum_{j=1}^{d} \int_{A_{j,t}}\frac{1}{|x_j|^p}\, dx \leq \int_{A_t} \frac{1}{|x|^p} \,dx$?
- Rigorous derivation of the long-time limit of oscillatory integrals
- Inverse of a Fourier Transform is $L^1 \cap L^{\infty}$
- Oscillating function with periodic change of sign and substraction of values
- An asymptotic for a simple oscillatory integral
- Estimating an integrand
- Stationary phase for retarded potentials in electromagnetism
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?