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Ei=−0.521 a.u. =α+1/√2β Ej=−0.585 a. u. =α+2√2β Determine α and β.

User KBog
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1 Answer

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Let's start by setting up the system of equations based on the information given:

1) α + 1/√2 * β = -0.521

2) α + 2√2 * β = -0.585

To solve this system of equations, we can rewrite the equations in matrix form:

[1, 1/√2] [α] = [-0.521]

[1, 2√2] [β] = [-0.585]

Now, this can be solved using a method of linear algebra which is to use matrix algebra. For this, we set up a 2x2 matrix A with coefficients of α and β on the left side of equations and a 2x1 matrix b with the constants Ei and Ej on the right side of the equations.

Matrix A will look like:
| 1 1/√2 |
| 1 2√2 |

Matrix b will look like:
| -0.521 |
| -0.585 |

Now, we can solve for [α, β] using a method of matrix algebra called 'solve' function. This function will solve the system of equations and will give us the values of α and β in the form of a solution vector.

The solution vector is (-0.4996666666666667, -0.030169889330625997)

So, α = -0.4996666666666667 and β = -0.030169889330625997.

User Dave Dopson
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