To have a prove of the Heisenberg uncertainty principle I have need to understand the operator commutator. My starting point is: $[A,B]=AB-BA \tag{a}$

Now, why must be

$$\left[\frac{\partial }{\partial x},x\right]\stackrel{?}{=}1 \tag{1}$$ I have thought, from the rule (a),

This identity $$\left[x,\frac{\partial }{\partial x}\right]=-1 \tag{2}$$ is easy because $[A,B]=-[B,A]$. I have not understood, also, (3) and (4) $$\left[i\hslash\frac {\partial}{\partial x},x\right]=i\hslash \tag{3}$$

$$[p_x,x]=i\hslash \tag{4}$$ where $p_x$ is the momentum on $x-$ axis.

Are very appreciated simple books where I can find very simple operations with these commutators because I have never studied quantum mechanics.

I thank in advance anyone who could help me to understand the commutators.

Considering that I've never studied quantum mechanics before I have need to understand the operator commutator. My start is: $[A,B]=AB-BA \tag{a}$

Now, why must be

$$\left[\frac{\partial }{\partial x},x\right]\stackrel{?}{=}1 \tag{1}$$ I have thought, from the rule (a),

This identity $$\left[x,\frac{\partial }{\partial x}\right]=-1 \tag{2}$$ is easy because $[A,B]=-[B,A]$. I have not understood, also, (3) and (4) $$\left[i\hslash\frac {\partial}{\partial x},x\right]=i\hslash \tag{3}$$

$$[p_x,x]=i\hslash \tag{4}$$ where $p_x$ is the momentum on $x-$ axis.

To be able to prove the Heisenberg uncertainty principle I have need to understand the operator commutator. My starting point is: $[A,B]=AB-BA \tag{a}$

Now, why must be

$$\left[\frac{\partial }{\partial x},x\right]\stackrel{?}{=}1 \tag{1}$$ I have thought, from the rule (a),

This identity $$\left[x,\frac{\partial }{\partial x}\right]=-1 \tag{2}$$ is easy because $[A,B]=-[B,A]$.

  I have not understood, also, (3) and (4) $$\left[i\hslash\frac {\partial}{\partial x},x\right]=i\hslash \tag{3}$$

$$[p_x,x]=i\hslash \tag{4}$$ $p_x$ is the momentum on $x-$ axis.

Are very appreciated simple books where I can find very simple operations with these commutators because I have never studied quantum mechanics.

I thank in advance anyone who could help me.

To have a prove of the Heisenberg uncertainty principle I have need to understand the operator commutator. My starting point is: $[A,B]=AB-BA \tag{a}$

Now, why must be

$$\left[\frac{\partial }{\partial x},x\right]\stackrel{?}{=}1 \tag{1}$$ I have thought, from the rule (a),

This identity $$\left[x,\frac{\partial }{\partial x}\right]=-1 \tag{2}$$ is easy because $[A,B]=-[B,A]$. I have not understood, also, (3) and (4) $$\left[i\hslash\frac {\partial}{\partial x},x\right]=i\hslash \tag{3}$$

$$[p_x,x]=i\hslash \tag{4}$$ where $p_x$ is the momentum on $x-$ axis.

Are very appreciated simple books where I can find very simple operations with these commutators because I have never studied quantum mechanics.

I thank in advance anyone who could help me to understand the commutators.

To be able to prove the Heisemberg uncertainty principle I have need to understand the operator commutator. My starting point is: $[A,B]=AB-BA \tag{a}$

Now, why must be

$$\left[\frac{\partial }{\partial x},x\right]\stackrel{?}{=}1 \tag{1}$$ I have thought, from the rule (a),

This identity $$\left[x,\frac{\partial }{\partial x}\right]=-1 \tag{2}$$ is easy because $[A,B]=-[B,A]$.

I have not understood, also, (3) and (4) $$\left[i\hslash\frac {\partial}{\partial x},x\right]=i\hslash \tag{3}$$

$$[p_x,x]=i\hslash \tag{4}$$ $p_x$ is the momentum on $x-$ axis.

Are very appreciated simple books where I can find very simple operations with these commutators because I have never studied quantum mechanics.

I thank in advance anyone who could help me.

To be able to prove the Heisenberg uncertainty principle I have need to understand the operator commutator. My starting point is: $[A,B]=AB-BA \tag{a}$

Now, why must be

$$\left[\frac{\partial }{\partial x},x\right]\stackrel{?}{=}1 \tag{1}$$ I have thought, from the rule (a),

This identity $$\left[x,\frac{\partial }{\partial x}\right]=-1 \tag{2}$$ is easy because $[A,B]=-[B,A]$.

I have not understood, also, (3) and (4) $$\left[i\hslash\frac {\partial}{\partial x},x\right]=i\hslash \tag{3}$$

$$[p_x,x]=i\hslash \tag{4}$$ $p_x$ is the momentum on $x-$ axis.

Are very appreciated simple books where I can find very simple operations with these commutators because I have never studied quantum mechanics.

I thank in advance anyone who could help me.