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## Homework Statement

Rewrite the state

**|ψ⟩ = √(1/2)(|0> + |1>)**in the new basis.

**|3⟩ = √(1/3)|0⟩ + √(2/3)|1⟩**

|4⟩ = √(2/3)|0⟩ − √(1/3)|1⟩

|4⟩ = √(2/3)|0⟩ − √(1/3)|1⟩

You may assume that |0⟩ and |1⟩ are orthonormal.

## Homework Equations

## The Attempt at a Solution

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I have a similar example in my notes however there is a step that I has stumped me. Annoyingly its the first one.

In my notes I have:

**"""**If we want to work in the basis |+⟩ and |−⟩ instead of | ↑⟩ and |↓⟩, with,

**|+⟩ = (1/√2)(| ↑⟩ + | ↓⟩)**&

**|−⟩ = (1/√ 2)(| ↑⟩ − | ↓⟩)**

how would |ψ⟩ and I be written in the new basis?

Let us rearrange as:

**| ↑⟩ = 1/(√2)(|+⟩ + |−⟩) &**

**| ↓⟩ = (1/√2)(|+⟩ − |−⟩)"""**

After rearranging I think that I should be able to complete the question but as it stands I cant see how to rearrange them to get |0> & |1>. Any advice would be much appreciated as really struggling with Dirac notation at the moment. Thanks 12x4